Study of the 238 U(d,p) surrogate reaction via the simultaneous measurement of gamma-decay and fission probabilities

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1 Study o the 238 U(d,p) surrogate reaction via the simultaneous measurement o gamma-decay and ission probabilities Q. Ducasse 1,2, B. Jurado 1,*, M. Aïche 1, P. Marini 1, L. Mathieu 1, A. Görgen 3, M. Guttormsen 3, A.. Larsen 3, T. Tornyi 3, J.. Wilson 4, G. Barreau 1, G. Boutoux 5, S. zajkowski 1, F. Giacoppo 3, F. Gunsing 6, T.W. Hagen 3, M. Lebois 4, J. Lei 7, V. Méot 5, B. Morillon 5, A. Moro 7, T. Renstrøm 3, O. Roig 5, S. J. Rose 3, O. Sérot 2, S. Siem 3, I. Tsekhanovich 1, G. M. Tveten 3, M. Wiedeking 8 1) EBG, RS/I2P3-Université de Bordeaux, hemin du Solarium B.P. 120, Gradignan, France 2) EA-adarache, DE/DER/SPR/LEPh, Saint Paul lez Durance, France 3) Department o Physics, University o Oslo, 0316 Oslo, orway 4) IP d Orsay, Bâtiment 100, 15 rue G. lemenceau, Orsay edex, France 5) EA DAM DIF, Arpajon, France 6) EA Saclay, DSM/Iru/SPh, Gi-sur-Yvette edex, France 7) Departamento de FAM, Universidad de Sevilla, Apartado 1065, Sevilla, Spain 8) ithemba LABS, P.O. Box 722, 7129 Somerset West, South Arica Abstract: We investigated the 238 U(d,p) reaction as a surrogate or the n U reaction. For this purpose we measured or the irst time the gamma-decay and ission probabilities o 239 U* simultaneously and compared them to the corresponding neutron-induced data. We present the details o the procedure to iner the decay probabilities, as well as a thorough uncertainty analysis, including parameter correlations. alculations based on the continuum-discretized coupledchannels and distorted-wave Born approximations were used to correct our data rom detected protons originating rom elastic and inelastic deuteron breakup. The corrected ission probability is in agreement with neutron-induced data, whereas the gamma-decay probability is much higher than the neutron-induced data. The perormed statistical-model calculations are not able to explain these results. PAS: y ; z I Introduction eutron-induced reaction cross sections o short-lived nuclei are important in several domains such as undamental nuclear physics, nuclear astrophysics and applications in nuclear technology. These cross sections are key input inormation or modeling stellar element nucleosynthesis via the s and r-processes. They also play an essential role in the design o advanced nuclear reactors or the transmutation o nuclear waste, or reactors based on innovative uel cycles like the Th/U cycle. However, very oten these cross sections are extremely diicult (or even impossible) to measure due to the high radioactivity o the targets involved. The surrogate-reaction method was irst developed at the Los Alamos ational Laboratory by ramer and Britt [1]. This indirect technique aims to determine neutron-induced cross sections o reactions involving short-lived nuclei that proceed through the ormation o a compound nucleus, i.e. a nucleus that is in a state o statistical equilibrium. In this method, the same compound nucleus as in the neutron-induced reaction o interest is produced via an alternative, or surrogate, reaction (e.g. a transer or inelastic scattering reaction). The surrogate-reaction method is schematically * jurado@cenbg.in2p3.r 1

2 represented in Fig. 1. The let part o Fig. 1 illustrates a neutron-induced reaction on target A-1, which leads to the ormation o nucleus A* at an excitation energy E*. The nucleus A* can decay via dierent exit channels: ission, gamma-decay, neutron emission, etc. On the right part o Fig. 1, the same compound nucleus A* is produced via a surrogate reaction. In Fig. 1, the surrogate reaction is a transer reaction between a projectile y (a light nucleus) and a target X, leading to the heavy recoil nucleus A* and an ejectile w. The charge and mass identiication o the ejectile w allows one to deduce the charge and mass o the decaying nucleus A*, and the measurement o the ejectile kinetic energy and emission angle provides its excitation energy E*. In most applications o the surrogate method, the surrogate reaction is used to measure the decay probability P χ and the desired neutron-induced reaction cross section is simulated by applying the equation: σ 1 ( E ) = σ ( E ) P ( E*) (1) A A A χ n n χ A where the index χ represents the decay mode (e.g. ission or gamma-ray emission) and σ ( En) is the cross section or the ormation o a compound-nucleus A by the absorption o a neutron o A energy E n by nucleus A-1. The compound-nucleus ormation cross section σ ( En) can be calculated with phenomenological optical-model calculations with an accuracy o about 10% or nuclei not too ar rom the stability valley [2]. The excitation energy E* and the neutron energy E n A 1 are related via the equation E* = Sn + En, where S n is the neutron separation energy o nucleus A A. Figure 1: (olor Online) Schematic representation o the surrogate-reaction method. The surrogate reaction depicted here is a transer reaction X(y,w)A*. Three o the possible exit channels (ission, gamma emission and neutron emission) are represented. One o the main advantages o the surrogate-reaction method is that, in some cases, one can ind a surrogate reaction where the target X is stable or less radioactive than the target A-1. However, the interest o the surrogate-reaction method goes well beyond the accessibility o the targets in directkinematics experiments. Indeed, due to the current impossibility to produce ree-neutron targets, surrogate reactions might be used to simulate neutron-induced reactions o very short-lived nuclei that are only available as radioactive beams. O particular interest is the (d,p) reaction, i.e. the transer o a neutron rom the weakly bound deuteron target to the radioactive beam, which intuitively appears as the closest reaction to a neutron-induced reaction in inverse kinematics. 2

3 For the surrogate-reaction method to be valid, several conditions have to be ulilled [2]. First, both the neutron-induced and the surrogate reactions must lead to the ormation o a compound nucleus. In that case the decay o nucleus A* is independent o the entrance channel and the reaction cross section can be actorized into the product o the compound-nucleus ormation cross section and the decay probability into a channel χ, as in eq. (1). The second condition is that the decay probability measured in the surrogate reaction has to be equal to the decay probability in the neutron-induced reaction. This is the case in at least two limiting situations: i the angular momentum (J) and parity (π) distributions populated in the neutron- and transer-induced reactions are the same, or i the decay probability o the compound nucleus is independent o its angular momentum and parity, which is the so-called Weisskop-Ewing limit. Since or most surrogate reactions it is not yet possible to determine the populated J π distribution, the validity o the surrogate method has to be veriied a posteriori, by comparing the obtained results with well known neutron-induced data. Surrogate-reaction studies perormed in the last decade have shown that ission cross sections obtained via the surrogate-reaction method are generally in good agreement with the corresponding neutron induced data, see e.g. [3] and other examples included in [2]. However, discrepancies as large as a actor 10 have been observed when comparing radiative-capture cross sections o rareearth nuclei obtained in surrogate and neutron-induced reactions [4, 5]. These signiicant dierences have been attributed to the higher angular momenta populated in the surrogate reaction. At excitation energies close to S n, neutron emission is very sensitive to the angular momentum o the decaying nucleus A* as only the ground state and the irst excited states o the residue nucleus A-1 can be populated. When the angular momentum o A* is considerably higher than the angular momentum o the irst states o A-1, neutron emission is hindered and the nucleus A* predominantly decays by gamma emission, which is the only open decay channel [5]. This eect is expected to be reduced or actinides, as they have more low-lying states than rare-earth nuclei, thus making neutron decay less selective. However, the radiative-capture cross section o 232 Th obtained via the 232 Th(d,p) surrogate reaction in re. [6] shows very large discrepancies with respect to the neutroninduced radiative-capture cross section at low neutron energies. Similarly to the situation at energies close to the ground state, the energy region close to the ission barrier is also characterized by a low density o states. Thereore, it is surprising that the spin/parity mismatch between the surrogate and neutron-induced reactions has no major impact on the ission probability. To shed light into this puzzling observation, it is irst o all necessary to demonstrate the much weaker sensibility o the ission probability to the reaction entrance channel by simultaneously measuring ission and gamma-decay probabilities or the same nucleus at the same excitation energy. This has never been done beore and is the aim o the present work. Here we concentrate on the 238 U(d,p) reaction, which is used to simulate the n+ 238 U reaction or which goodquality neutron-induced data on ission and capture cross sections exist. The measurement o the gamma-decay probability at excitation energies where the ission channel is open is challenging because o the background o gamma rays emitted by the ission ragments. Above S n, the gammadecay probability o 239 U decreases very rapidly with the excitation energy, whereas the ission probability increases. Thereore, the raction o gamma rays coming the ission ragments increases gradually with E* until they represent most o the detected gamma rays. In this work, we restricted the measurement o the gamma-decay probability to the range E* < S n +1.5 MeV, in order to limit the uncertainty due to the subtraction o the ission-ragment gamma-ray background. 3

4 The (d,p) reaction presents a diiculty. Britt and ramer [7] noticed that, above a certain excitation energy, the ission cross sections obtained via the (d,p) surrogate reaction were signiicantly lower than the corresponding neutron-induced cross section. They attributed it to the elastic breakup o the deuteron. Deuteron breakup is actually a rather complex process and has recently been the subject o several theoretical works, see e.g. [8, 9]. Thereore, our data can also be used to test these new calculations. In addition, our experimental conditions are dierent rom the ones o Britt and ramer. II Experiment The experiment was perormed at the Oslo yclotron Laboratory that provided a deuteron beam o 15 MeV energy with an intensity o about 4 ena. The setup is sketched in Fig. 2. The multi-strip ΔE/E silicon telescope SiRi [10] was used to identiy the ejectiles and determine their kinetic energies and angles. SiRi covered polar angles ranging rom 126 to 140 in steps o 2 degrees. An ensemble o our PPAS [11], located at orward angles, was used to detect the ission ragments in coincidence with the ejectiles. The reaction chamber housing SiRi, the PPAs and the 238 U target was surrounded by the ATUS array [12], constituted o 27 high-eiciency ai detectors placed 22 cm away rom the target. ATUS was used to detect gamma rays with energies ranging rom ew hundreds o kev to about 10 MeV emitted in coincidence with the ejectiles. A 21 µm thick aluminum oil was placed in ront o the SiRi telescope to stop ission ragments. The ampliied signals o the telescopes, and the ission and gamma detectors were digitized with an analog-todigital converter. All the detector signals were pulse-shaped into ast timing signals and sent to a time-to-digital converter to measure the time dierences between the telescopes and the ission and gamma detectors. The acquisition system was triggered by a logic OR o the E-E coincidences o each telescope strip. Figure 2: (olor Online) Schematic view o the setup used at the Oslo yclotron Laboratory or the simultaneous measurement o ission and gamma decay-probabilities. We used a high-quality metallic 238 U target, with 99.5% isotopic purity, produced by the GSI target laboratory. It had a thickness o 260 µg/cm 2 and was deposited on a 40 µg/cm 2 natural carbon layer. Great care was taken to avoid as much as possible the oxidation o the target, which was produced only a ew days beore the measurement and was transported rom GSI to Oslo under vacuum 4

5 conditions. III Data analysis The decay probability in the outgoing channel χ o the 239 U* nucleus produced in the 238 U(d,p) reaction can be obtained as : χ ( E*) Pχ ( E*) = (2) S ( E*) ( E*) Here S (E*) is the so-called singles spectrum, i.e. the total number o detected protons as a unction o excitation energy E*. χ ( E*) is the coincidence spectrum, corresponding to the number o protons detected in coincidence with the observable that identiies the decay mode, e.g. a ission ragment or a gamma ray, and ε χ is the associated detection eiciency. In the absence o protons originating rom contaminant reactions, the quantity S (E*) corresponds to the total number o ormed 239 U* nuclei and ( E*) /ε χ to the number o 239 U* nuclei that have decayed via channel χ χ. The ollowing sections discuss how the quantities involved in eq. (2) are obtained. ε χ Figure 3: (olor Online) Energy loss versus residual energy o the ejectile measured at 126 degrees. The ejectiles corresponding to dierent hydrogen isotopes are indicated. The arrows in the lower part indicate the 17 O and 13 states used or the energy calibration o the telescopes, where 13 0 corresponds to the ground state o 13, 13 1 to the irst excited state, etc. A Excitation energy The excitation energy o 239 U* is determined rom the measured kinetic energy and emission angle 5

6 o the protons, by applying energy and momentum conservation laws. Figure 3 shows an identiication plot representing the energy loss in the ΔE detector as a unction o the residual energy in the E detector o the ejectiles measured in one strip o the silicon telescope. The dierent ejectiles corresponding to dierent transer channels (and dierent uranium isotopes) can be well distinguished. Interactions o the deuteron beam with oxygen contamination and the carbon backing o the target lead to the production o O and isotopes in their ground and excited states. Some o those states can be observed as well-separated peaks in the identiication plot, and correspond to well-deined energies o the ejectiles. The ejectile energies corresponding to the ormation o 17 O in the ground state by the 16 O(d,p) reaction and several 13 states populated in the 12 (d,p) reaction have been used to calibrate in energy the SiRi telescope. The calibration procedure was validated by comparing our calibrated singles spectrum with the spectrum measured by Erskine [13]. The excitation-energy resolution was estimated rom the standard deviation o the peaks associated to the 238 U(d,d ) reaction and amounts to about 50 kev. Figure 4: (olor Online) umber o detected protons as a unction o the excitation energy o 239 U* measured at 126 degrees. The blue dashed line is the proton spectrum, p. The red dashed-dotted line, c, corresponds to the spectrum obtained with the carbon backing without normalization actor. The spectrum obtained ater subtraction o the carbon spectrum, p-c, is represented by the pink dotted line. The singles spectrum S is shown as a black solid line. The vertical dotted line represents the neutron separation energy o 239 U. The peaks related the ormation o 17 O and 13 in the ground- and irst excited states are indicated with the same notation as in Fig. 3. B Singles spectrum To determine the singles spectrum we irst selected the protons via the identiication plot shown in Fig. 3 and represented the number o protons as a unction o the excitation energy o 239 U*. This 6

7 spectrum is called the proton spectrum p and is represented in blue in Fig. 4. The peaks above 4 MeV correspond to protons originating rom reactions on the carbon backing and the oxygen o the target. The dierent steps undertaken to remove these contaminant events are illustrated in Fig. 4. First we subtracted rom the p spectrum the proton spectrum, appropriately normalized, obtained in a separated measurement with the carbon backing only, the c spectrum. The spectrum that results rom the subtraction is labelled as p-c in Fig. 4. Because the shape o the carbon peaks in the p and c spectra was not identical, the carbon peaks could not be completely removed rom p, as can be seen in Fig. 4. To remove these peak residues and the oxygen peaks, or which a background measurement cannot be perormed, the p-c spectrum was interpolated below the contaminant peaks with a polynomial unction. To determine the shape o the polynomial we exploited the angular dependence o the kinetic energy o the emitted protons. This dependence is much stronger or protons ejected in reactions on light nuclei such as and O than on the heavy 238 U nucleus. Thereore, the contaminant peaks move to higher excitation energies o 239 U* as the detection angle increases. Thus, the shape o the singles spectrum below the contaminant peaks at a given angle was deduced rom the shape o the proton spectrum measured at a dierent angle. The interpolation procedure was only applied in the vicinity o S n, which is the region o interest in the present work. The singles spectrum s is shown as the solid black line in Fig. 4, it represents the spectrum o protons coming rom reactions on the 238 U target. Figure 5: (olor Online) The red dotted line, c raw, is the spectrum o protons detected in coincidence with a signal in the ission detector as a unction o the excitation energy o 239 U*. The c blue dashed-dotted line corresponds to the normalized random-coincidence spectrum,. The ission coincidence spectrum, Fission coincidence spectrum Figure 5 shows the spectrum c raw, is shown as the solid black line. with a signal in any o the our PPAs. This spectrum presents an intense peak at about 8 MeV 7 random that results rom selecting the protons detected in coincidence

8 excitation energy. This peak corresponds to random coincidences between protons originating rom reactions on the carbon backing and the ission detectors. To remove these random events we subtracted rom the coincidence spectrum the spectrum (properly normalized) obtained when c selecting the events with a time dierence lying outside o the coincidence window,, see 8 random [14] or details. The result is the ission coincidence spectrum ( E *), shown as a solid black line in Fig. 5. D Fission-detection eiciency The ission-detection eiciency, ε (E*), is the last term o eq. (2) needed to iner the ission-decay probability o 239 U*. The ission-detection eiciency is determined by the solid angle covered by the our PPAs (the so-called geometrical eiciency) and by the angular anisotropy o the ission ragments in the laboratory reerence system. The latter is given by the angular anisotropy o the ragments in the center o mass (M) system corrected or kinematical eects due to the recoil energy o the issioning nucleus. The geometrical eiciency was measured with a 252 source o known activity and was ound to be (41.1 ± 0.3)% o 4π. The PPAs used in this experiment were not position-sensitive detectors and the angular anisotropy in the M could not be measured. Thereore, we used the angular anisotropy in the M measured by Britt and ramer [7] or the 238 U(d,p) reaction at 18 MeV deuteron incident energy. To include the angular anisotropy eects, we perormed a Monte-arlo simulation that reproduces the geometrical eiciency. In the simulation, the velocities o the ission ragments in the M were taken rom the GEF code [15]. The total eiciency obtained with our simulation is ε = (48.0 ± 3.5)%. We considered a constant eiciency since the variation o the eiciency with the excitation energy is very weak and is largely included in the inal uncertainty. The inal uncertainty on the ission eiciency is dominated by the uncertainty on the angular anisotropy in the M that has been numerically propagated into the inal eiciency via the Monte-arlo simulation. E Gamma-coincidence spectrum To obtain the gamma-decay probability we need to determine the number o ormed 239 U* nuclei that decay through a gamma-ray cascade, γ ( E*), i.e. the number o 239 U* nuclei that de-excite by emitting gamma rays only. The eiciency o the ATUS array is about 14.5% at 1.33 MeV gamma-ray energy. Thereore, in most cases, we detected only one gamma ray per cascade. For the ew cases where more than one ai detector was hit in one event, we randomly selected one detector signal amplitude in the oline data analysis. In that way, we avoided counting more than one gamma ray per cascade. To calibrate in energy the ai scintillators we used the gamma rays emitted in the de-excitation o several excited states o 13 and 17 O populated by the (d,p) reaction. As mentioned in the introduction, we restricted the measurement o the gamma-decay probability to E* < S n +1.5 MeV. th For this reason, a threshold, E γ =1.5 MeV, was applied to the detected gamma rays in order to eliminate the gamma rays originating rom the residue nucleus 238 U* produced ater neutron emission rom 239 U*. This threshold is shown in the two-dimensional plot in Fig. 6 representing the excitation energy o 239 U* versus the measured gamma-ray energy. The gamma rays emitted by the

9 238 U* residue are on the let side o the diagonal line which intersects the E* axis at S n, whereas the gamma rays emitted by the 239 U* nucleus are on the let side o the diagonal line with origin at E*=0. The region used or the determination o the gamma-decay probability is represented by the red dashed line. The spectrum detected gamma ray with energy above, tot γ corresponding to the coincidences between protons and one th E γ is shown as a blue dashed-dotted line in Fig. 7. The same procedure as the one described in Section was used to remove random coincidences. As, tot expected, the coincidence spectrum γ shows a step decrease at S n because neutron emission starts to compete with gamma emission. Figure 6: (olor online) Excitation energy o 239 U versus detected gamma-ray energy. The applied th energy threshold, E γ, is represented by the vertical dotted line. Excitation energies corresponding th to S n and S n + E γ are indicated by horizontal dotted lines. The 45-degree lines with origin at E* = 0 and E* = S n are represented by ull lines. The region used in the analysis o the gamma-decay probability is highlighted by the red dashed line. A time window o 11 ns was used or selecting the proton-gamma-ray coincidences. This time window in combination with the 1.5 MeV gamma-ray energy threshold allowed us to remove the majority o the contaminant gamma rays emitted by the a and I nuclei o the scintillator material ater the capture o a neutron emitted by 239 U*. Indeed, in the excitation-energy range o interest, the maximum kinetic energy carried by the neutron is E n,max = E* - S n = 1.5 MeV. onsequently, only neutrons with lower kinetic energies can be captured in the ai detectors. Taking into account 9

10 the time resolution o the ATUS ai detectors o about 10 ns and the average interaction distance o the neutrons in the ai crystals o 25 cm [6], the time window o 11 ns suppresses 95% o the emitted neutrons with E n 0,360 MeV and 68% with E n 1 MeV. Above a ew hundred kev the neutron inelastic cross sections o a and I are one or more orders o magnitude larger than the capture cross sections, but the gamma rays originating rom inelastic scattering on a and I are also removed by the 1.5 MeV gamma-ray energy threshold. To demonstrate the absence o gamma rays coming rom the interaction o neutrons emitted by 239 U* with the ai detectors, we analyzed the data using a time window o 24 ns which would in principle lead to an increase o the gamma-decay probability due to the presence o more contaminant gamma rays coming rom neutron capture in the ai. However, the results agree within the error bars. In act, the contribution rom capture events in the ai starts to be signiicant only when a time window as large as 42 ns is used. The latter window includes a large contribution o neutrons with E n < 200 kev or which the capture cross sections are rather high., tot Figure 7: (olor online) The blue dashed-dotted line γ represents the number o protons detected in coincidence with a gamma ray detected in any o the ATUS detectors as a unction o the excitation energy o 239 U measured at 126 degrees. A threshold in the gamma-ray energy > 1.5 MeV and a time window o 11 ns were used to obtain this spectrum. The red-dotted line is the ission-gamma coincidence spectrum γ, divided by the ission eiciency ε. The black line represents the gamma-coincidence spectrum The arrow indicates the neutron separation energy o 239 U*. th E γ γ. The green dashed line is the singles spectrum S. The total gamma-coincidence spectrum, tot γ has to be corrected or the prompt gamma rays 10

11 emitted by the ission ragments. The impact o gammas originating rom the ission ragments can be noticed on Fig. 7, where we observe an increase o the coincidence spectrum,, tot γ, above about 6 MeV corresponding to the onset o ission. This correction can be done by measuring triple coincidences between protons, ission ragments and gamma rays. The corrected coincidence spectrum γ is then obtained as: E ( E*) = ( E*) (3) γ,, ( *) tot γ γ ε ( E*) where γ, is the number o gamma cascades detected in coincidence with a proton and a ission ragment, and γ is the inal gamma-coincidence spectrum shown as a solid line in Fig. 7. Figure 8: (olor online) Ratio between the gamma-coincidence and the singles spectra. The vertical dotted line indicates the neutron separation energy and the red solid line is a linear it to the data in the E* interval [2 MeV; S n ]. F Gamma-cascade detection eiciency To obtain the gamma-decay probability, one needs to determine the eiciency or detecting a gamma cascade rather than the eiciency or detecting a gamma o a particular energy. In this work, we used the EXtrapolated Eiciency Method (EXEM) developed in [16] to determine the gammacascade detection eiciency. In a surrogate reaction it is possible to populate excitation energies below the neutron separation energy. For a neutron-rich nucleus as 239 U*, that does not ission nor emits protons below S n, the only possible de-excitation mode at E* < S n is gamma decay. Thereore, the gamma-decay probability is equal to 1: γ ( E*) Pγ ( E*) = 1 = or E*<S S n (4) ( E*) ε ( E*) γ 11

12 From eq. (4) it ollows that: γ ( E*) ε γ ( E*) = or E*<S S n (5) ( E*) Thus, or excitation energies below S n, the gamma-cascade detection eiciency, ε γ (E*), can be directly obtained rom the ratio between the gamma-coincidence and the singles spectra. For medium-mass and actinide nuclei in the region o continuum level densities there is no reason to expect a drastic change at S n o the characteristics o the gamma cascades (multiplicity and average gamma energy), and thus o ε γ (E*). This is the main idea on which the EXEM is based. The EXEM assumes that the dependence o the gamma-cascade detection eiciency ε γ on E* measured below S n can be extrapolated to excitation energies above S n. This is illustrated in Fig. 8, where the ratio o the gamma-coincidence and the singles spectra is shown together with a linear it. The values o the it unction evaluated at E* above S n gave us the gamma-cascade eiciency used to determine the gamma-decay probability. In the excitation-energy range o interest, the gamma-cascade detection eiciency increases rom a value o about (6.5±0.5)%, near S n, to about (8.5±0.7)% at E*=6.3 MeV. The uncertainty on ε γ above S n was obtained rom the uncertainties on the it parameters. The validity o the EXEM applied to the actinide region is demonstrated in [17]. In particular in [17], we present statistical-model calculations o the average gamma energy and multiplicity as a unction o excitation energy or 239 U*. These calculations show that there is no change in the slope o these two quantities above S n and that the linear increase o the eiciency is mainly due to a linear increase o the average multiplicity. G Uncertainty analysis onsidering eq. (2), the relative uncertainty o P χ at a given E* is given by: Var( P ( E*)) Var( ( E*)) Var( ε ( E*)) S χ χ Var( ( E*)) χ = S ( Pχ( E*) ) ( χ ( E*) ) ( ( E*) ) ( ε χ( E*) ) S S ov( ( E*); χ ( E*)) ov( χ ( E*); εχ( E*)) ov( ( E*); εχ( E*)) S S ( E*) ( E*) ( E*) ε ( E*) ( E*) ε ( E*) χ χ χ χ (6) where Var and ov represent the variance and the covariance o the measured quantities, respectively. We have shown in [14] that or the ission probability our experimental procedure allows us to disregard the two last covariance terms in eq. (6), but that the covariance between single and coincidence events has a signiicant impact on the inal uncertainty. In this work, we present a procedure to determine the covariance terms between the measured quantities that is dierent rom the mathematical procedure described in [14]. Our new procedure allowed us to extract the covariance terms associated to the gamma-decay probability in a straightorward manner. For simplicity, in the ollowing equations we will omit the dependence on E* o all the measured quantities. To illustrate our alternative approach we will consider the case o ov( S ; ), keeping in mind that this procedure can be used to obtain the covariance o any other two quantities involved in the 12

13 measurement o the decay probabilities. The covariance ov( S ; luctuations in S aect the value o ) is a measure o how. One way to determine it is by repeating the measurements in exactly the same experimental conditions (geometry, beam intensity, measuring time, etc.) and by representing the measured S versus. Even though the experimental conditions are identical, S and will luctuate, because they are random variables that ollow Poisson statistics. O course, this procedure is generally not done. Alternatively, one can use the data collected during the experiment to construct groups o independent measured events with values or S that are sampled rom a Gaussian distribution centered at a given value o < S > (e.g. 200) and with a standard S deviation equal to < >. In this way, one simulates how S would have varied i one would have perormed exactly the same experiment many times. Figure 9 a) shows the impact o the variation o S on the measured values o A S = on the measured values o and Fig. 9 b) shows the impact o varying the quantity. The quantities A and are uncorrelated and their corresponding covariance term is zero. The comparison o parts a) and b) o Fig. 9 allows one to asses the dierences in the characteristic pattern o two variables that are correlated (Fig. 9 a) and uncorrelated (Fig. 9 b). To obtain the plots o Fig. 9, we have used independent groups o experimental data in an E* region ree o events coming rom contaminant reactions. The variance and covariance terms are then determined with the estimators: n 1 Var( ) = ( i ) n i= 1 (7) n S 1 S S ov( ; ) = ( i )( i ) n where n is the number o groups o data (or the number o points on Fig. 9) and the average quantities <> are given by ov( S ; ) Var( 1 n i n i = 1 i= 1 =. When we apply this experimental procedure we obtain ), in agreement with the result obtained in [14]. For the gamma-decay probability, the two last covariance terms in eq. (6) cannot be in principle neglected because ε γ has been obtained with the EXEM which involves the S and γ variables. Moreover, because o the subtraction o prompt-ission gamma rays, we have to consider three additional covariance terms. Indeed, rom eq. (3) it ollows: Var 2, tot Var,, tot γ γ, Var ε ov γ γ, ( γ ) = Var( γ ) ε ε ε ( ε ), tot ov( ; ) (, ; ) γ ε ov γ ε γ, 2 γ, ε ε ( ) ( ) ( ; ) (8) 13

14 Figure 9: Measured as a unction o S (a) and as unction o A S = (b). The values o S have been sampled rom a Gaussian distribution centered at < S > =200 and with standard S deviation = 200. We have used the described experimental procedure to determine all the covariance terms needed to evaluate the uncertainty o P γ. We obtain that the covariance terms involving ε γ are a actor 10-3 smaller than the other covariance terms and can also be neglected. Thereore, only one additional covariance term,, tot ov( γ ; γ, ), has to be considered or the determination o the uncertainty on P γ. The results o the covariance analysis are listed on Table 1. ovariance P γ P S ov( ; χ ) Var( γ ) Var( ) S ov( ; ε ) 0 = 0 χ ov( χ ; ε χ ) 0 = 0 ov, tot ( γ ; γ, ),, ( tot ; ) Var( γ ) - ov γ ε = 0 - ov( γ ; ε ) = 0 -, Table 1: ovariance terms necessary to determine the uncertainty on the decay probabilities P χ, the index χ reers to either ission or gamma decay. In our experiment, the probabilities were measured at dierent excitation energies with the same setup. This introduces a correlation between the probabilities measured at dierent energies, and E, which must be accounted or. As shown in [14]: * j * E i syst * syst * Var(P ( )) (P ( )) * * χ Ei Var χ E j orr( Pχ( Ei ); Pχ( Ej )) = i i j * * Var(P ( E )) Var(P ( E )) χ i = 1 i i = j χ j (9) 14

15 syst * where Var(P χ ( E i )) corresponds to the systematic part o the total variance o the decay probability at energy E. Eq. (9) says that the correlation measures the importance o the systematic uncertainty * i with respect to the total uncertainty. It is close to 1 when the systematic uncertainty dominates the total uncertainty. In our measurement, the systematic uncertainty comes rom the uncertainty on the ission detection eiciency and rom the presence o contaminant peaks in the singles spectrum. IV Results and discussion Fig. 10 shows the results or the gamma-decay and ission probabilities. As already mentioned, our setup allowed us to measure the decay probabilities at eight dierent angles. We observe a decrease o the gamma-decay probability with increasing angle, whereas or the ission probability we observe an increase in the region rom 6.1 to 6.5 MeV. For the sake o clarity in Fig. 10 a) and b) we show only the decay probabilities measured at the limiting angles 126 and 140 degrees. We can see that the dierences between the decay probabilities measured at these two angles are signiicant. The possible origin o these dierences will be discussed in section IV B. Figure 10: (olor online) Measured gamma-decay (a) and ission (b) probabilities as a unction o excitation energy (symbols) compared to the results o several evaluations (lines). orrelation matrix or the gamma-decay (c) and ission (d) probabilities measured at 126 degrees. The vertical dotted line in panel a) represents the neutron separation energy o 239 U*. In Fig. 10 panels c) and d) the correlation matrices or the gamma-decay and ission probabilities 15

16 measured at 126 degrees are shown. They are representative o the correlation matrices or all the other detection angles. For the gamma-decay probability the correlation is the highest at the lowest excitation energies near S n. This is due to the act that the statistical uncertainty o the gamma-decay probability increases with excitation energy and the systematic uncertainty is larger near S n, due to the presence o contaminant peaks in the singles spectrum. On the contrary, or the ission probability the correlation is the highest at high excitation energies. The reason is that the statistical uncertainty on the ission probability decreases with excitation energy and the systematic uncertainty on the ission eiciency gives the strongest contribution to the total uncertainty at the highest excitation energies. In Figures 10 a) and b), our data are compared to the neutron-induced decay probabilities given by dierent evaluations. The latter have been obtained by dividing the evaluated neutron-induced cross sections by the compound-nucleus ormation cross section σ, according to eq. (1). σ was obtained with the phenomenological optical-model potential used in the JEDL 4.0 evaluation [18]. The gamma-decay probability obtained with the surrogate method is several times higher than the neutron-induced one over the whole excitation-energy range. The discrepancies between the surrogate data and the neutron-induced data decrease with excitation energy. A minimum actor o about 3 is reached near 6.3 MeV. The ission probability obtained with the surrogate reaction is in good agreement with the neutron-induced data below about 6 MeV. Above 6 MeV the JEDL and EDF evaluations are in very good agreement and show signiicant dierences with respect to the JEFF evaluation. Between 6 and 6.3 MeV our data are in better agreement with the JEFF evaluation. Above 6.3 MeV our results are systematically below the neutron-induced results. We observe dierences up to 30-35%. The reason or the discrepancy with respect to the neutroninduced data may be the deuteron breakup, which leads to a background o sterile protons that contaminates the singles proton spectrum. These protons are not related to the ormation o a compound nucleus 239 U* and lead to a decrease o the measured ission probability, as shown by eq. (2). This hypothesis was already put orward by Britt and ramer [7], but only now it starts to attract theoretical eorts [8, 9]. Interestingly, the data by Britt and ramer [7] obtained using the same 238 U(d,p) reaction with a beam energy o 18 MeV and protons detected at 150 degres are 30% lower than our data at the ission plateau. The impact o deuteron breakup on the ission probability at 15 and 18 MeV incident energies is evaluated in section IV A. Because the oxidation o the target could not be completely avoided, usion o the deuteron beam with oxygen and the subsequent evaporation o protons have also to be taken into account. Again, this leads to the production o sterile protons in the excitation-energy range o interest, decreasing the measured ission probability. Thereore, this process might also be responsible or the dierences observed between the surrogate data and the neutron-induced data, as well as between the two surrogate-reaction results. Indeed, as mentioned above, in our experiment we limited as much as possible the oxidation o the 238 U metallic target, whereas the 238 U target used by Britt and ramer was an oxide. With the help o the PAE4 code [19], we estimated that in our case the raction o protons originating rom usion-evaporation on oxygen is o the order o 10%. To obtain this value we used the number o oxygen atoms in the target that results rom counting the number o elastically scattered deuterons on oxygen, which can be seen on Fig. 3, and using the corresponding Rutherord-scattering cross section. This estimation leads to a raction o about two oxygen nuclei per three uranium nuclei in the target. ote that the contribution to the singles spectrum o the protons evaporated ater the usion o the deuteron with the carbon nuclei o the 16

17 target backing is removed when the carbon-backing spectrum c is subtracted rom the proton spectrum p, see section III. B. We do not know the chemical composition o the target used by Britt and ramer, but in view o the possible chemical orms o uranium oxide (UO 2, UO 3, UO 4 and U 3 O 8 ) we can say that there were at least two atoms o oxygen per uranium atom. This corresponds to a actor 3 more oxygen than in our target and thus to at least about 30% o protons originating rom usion-evaporation reactions on oxygen. Thereore, the larger amount o oxygen in the target used by Britt and ramer might explain, at least partly, the dierences between the two sets o surrogate-reaction data. A Deuteron breakup In principle, the (d,p) reaction can be seen as a two-step process in which, irst, the deuteron breaks up and then the neutron is absorbed by the target nucleus. However, this picture is way too simple. In act, the deuteron breakup is a rather complex process. One has to distinguish between elastic and inelastic breakup. In the elastic breakup (EB), the impinging deuteron breaks up due to the oulomb and/or nuclear interaction with the target, and the resulting proton and neutron move apart leaving the target nucleus in the ground state. The non-elastic breakup (EB) includes the processes in which the incident deuteron breaks up and the resulting proton and neutron move apart leaving the target nucleus in an excited state; the direct stripping o the neutron, and the usion o the breakup neutron with the target nucleus which leads to the compound-nucleus ormation. The latter mechanism, that we will call breakup usion (BF), is the one o interest in the context o the surrogate-reaction method. In an inclusive measurement, as ours, where only the proton is detected, it is not possible to experimentally discriminate the dierent processes. Thereore, here we rely on theory to estimate the contributions o the dierent mechanisms to the measured proton singles spectrum. Figure 11: (olor online) alculated contributions to the total deuteron breakup process (TB), as a unction o the excitation energy o 239 U or a deuteron beam energy o 15MeV and a proton angle o 140 degrees (a) and or a beam energy o 18 MeV and proton angle o 150 degrees (b). EB corresponds to non-elastic breakup, BF to breakup usion and EB to elastic breakup. ote that TB = EB + EB. The vertical dotted lines indicate the neutron separation energy o 239 U. 17

18 The breakup process was the subject o intense theoretical work in the eighties. Udagawa and Tamura [20] described the A(d,p) reaction within the distorted-wave Born approximation (DWBA) in prior orm, whereas Ichimura, Austern and Vincent [21] used the post-orm DWBA. The equivalence o the post and prior ormulations was irst demonstrated in the original work o Ichimura, Austern, and Vincent [21], although the prior-orm ormula derived in [21] diered rom that proposed by Udagawa and Tamura. Both approaches have in common that the non-elastic breakup cross section is proportional to a matrix element <ψ n W na ψ n > where ψ n is the wave unction describing the evolution o the neutron and W na is the imaginary part o the optical potential between the neutron and the nucleus A. In a recent publication, Potel et al. [8] discuss the equivalence between the post and prior methods and present results or the elastic and non-elastic breakup cross section o the 93 b(d,p) reaction. However, this study does not give the separated contribution rom BF. In this work, the EB contribution has been obtained with the continuum-discretized coupledchannels (D) method, using the coupled-channels code FRESO [22]. We have used the model o Ichimura, Austern and Vincent to determine the EB [9]. To estimate the BF part, the imaginary part o the potential W na has been divided into two parts, a part W na corresponding to the compound-nucleus ormation and a part associated to all the other remaining processes included in the EB. W na was parametrized in terms o a Woods-Saxon orm, with the parameters adjusted to reproduce the compound-nucleus ormation cross section as predicted by the JEDL 4.0 evaluation [18]. The results o our calculations or 15 and 18 MeV deuteron incident energies and 140 and 150 degrees, respectively, are shown in Fig. 11. The results or 15 MeV and 126 degrees are not shown because they are very close to the results obtained or 140 degrees. Because o the kinematics o the breakup process, there are no protons stemming rom the breakup process at E* < S n. It was argued in [23] that the approach o Udagawa and Tamura only gives the so-called "elastic breakup usion", that is, the BF not accompanied by the simultaneous excitation o the target. Thereore, the Udagawa and Tamura approach gives a lower limit o the BF contribution, as it excludes processes in which a compound nucleus is ormed ater target excitation. This is indeed the case, since the BF cross section we obtained with the Udagawa and Tamura approach is about 4% smaller than the one obtained with the Ichimura, Austern and Vincent method o re. [9]. The relative contribution o the dierent processes to the total cross section or both incident energies and detection angles is rather similar, see Fig. 11. In the region o interest in this work, E* < (S n +1.5) MeV, the elastic breakup represents less than 5 % o the total breakup, whereas the breakup usion represents nearly 80 %. The total breakup (TB), given by the sum o the elastic and inelastic breakup, can be directly related to the proton singles spectrum above S n. Thereore, these calculations allowed us to correct the singles spectrum rom the sterile protons originating rom corr elastic and non-elastic breakup. The corrected decay probabilities P c have been obtained in the ollowing way: meas P ( *) ( *) corr c E s TBU E Pc ( E*) = (10) s ( E*) BF where meas P χ is the measured decay probability. Eq. (10) implies the assumption that contributions 18

19 other than BF to the EB lead neither to ission nor to gamma emission. This is reasonable or the ission exit channel but it is rather probable that the 238 U* and 239 U* nuclei that are excited by the other processes emit gamma rays. Thereore, the corrected gamma-decay probability should be considered as an upper limit o the real gamma-decay probability. The corrected decay probabilities measured at 140 degrees are presented in Fig. 12. Obviously, the disagreement between the gamma-decay probability obtained with the 238 U(d,p) reaction and the neutron-induced data increases when the breakup correction is applied. On the other hand, the corrected average ission probability is in better agreement with the neutron-induced data. However, in the ission plateau, the corrected ission probability is still lower by about 15% than the neutroninduced data represented by the JEDL and EDF evaluations. This dierence may be attributed to the contribution rom protons originating rom usion-evaporation on oxygen, described above. When the ission probability measured by Britt and ramer [7] is corrected, the resulting ission probability is still signiicantly lower than the neutron-induced data. However, this does not mean that the breakup calculations or this case are incorrect, since the remaining dierence might be attributed to protons coming rom usion-evaporation on oxygen, which can be numerous due to the complete oxidation o the target used in [7]. Figure 12: (olor online) Measured mes P χ and corrected 19 corr P c decay probabilities as a unction o excitation energy. The neutron-induced decay probabilities rom dierent evaluations are represented by the lines. The gamma-decay probabilities are shown in panel a) and the ission probabilities in panel b). The vertical dotted line in panel a) indicates the neutron separation energy o 239 U. B omparison with statistical model calculations Figure 13 shows the breakup-corrected ission probability and the gamma-decay probability obtained in the surrogate reaction at 140 degrees together with the neutron-induced probabilities in the excitation-energy region where gamma emission and ission are in competition. In this energy range, the corrected ission probability is in good agreement with the neutron-induced data, whereas the gamma-decay probability obtained with the (d,p) reaction is several times higher than the neutron-induced one. These results indicate that the ission probability is much less sensitive to dierences in the entrance channel than the gamma-decay probability. The objective o this section

20 is to investigate whether we can explain this inding within the rame o the statistical model. For this purpose we have used the EVITA code, which is a Hauser-Feshbach monte-carlo code developed at the EA DAM that uses the same ingredients as the TALYS code [24]. The parameters o the EVITA code have been careully tuned to reproduce the experimental neutron-induced data. In act, the EVITA results are very close to the JEFF evaluation shown in Figs. 10, 12 and 13. Figure 13: (olor online) Fission and gamma-decay probabilities as a unction o excitation energy compared to the corresponding neutron-induced decay probabilities according to dierent evaluations. ote that only the ission probability has been corrected or deuteron breakup. Figure 14 shows the gamma-decay and ission probabilities calculated with the EVITA code or given initial values o spin and parity o the nucleus 239 U* in the region where both decay channels compete. The calculated gamma decay probabilities increase considerably with the spin o the decaying nucleus. This is mainly due to the hindering o neutron emission discussed in the introduction. On the other hand, the calculated ission probabilities decrease considerably with the angular momentum because the transition states on top o the ission barriers with the higher spins lie at higher excitation energies, leading to higher eective ission barriers. The calculations show that the parity o the states does not modiy these major trends. Let us now go back to Fig. 10 where we compared the decay probabilities measured at 126 and 140 degrees and use the EVITA results rom Fig. 14 or interpretation. One could explain the observed dierences as the result o the variation o the populated spin distribution with the angle o the ejectile. Our results would suggest that the mean angular-momentum populated when the ejectile is emitted at 126 degrees is somewhat higher than the one populated when the ejectile is emitted at 140 degrees. 20

21 Figure 14: (olor online) Decay probabilities as a unction o excitation energy or dierent values o angular momentum and parity o 239 U* calculated with EVITA. The decay probabilities measured in this work (ull circles) and the neutron-induced decay probabilities obtained with EVITA (thick blue lines) are also shown. Gamma-decay probabilities with positive and negative parities are shown in panels a) and b), respectively. Fission probabilities are shown in panels c) and d). As shown in Fig. 14, the ission probabilities measured in this work and calculated with EVITA agree both rather well with the ission probability obtained with an initial spin o about 3/2. However, our gamma-decay probability is best reproduced by the calculations with an angular momentum between 9/2 and 13/2, whereas the neutron-induced gamma-decay probability is best reproduced when the initial spin is between 1/2 and 3/2. Thereore, we ind a clear inconsistency as the EVITA calculations cannot reproduce our measured ission and gamma-decay probabilities with a unique initial spin distribution. To illustrate this in a more quantitative way we have used the calculated decay probabilities P χ (E*,J π ) shown in Fig. 14 to it the decay probabilities with the expression: 2 ( J J ) 1 2 2σ π Pχ( E*) = e Pχ( E*, J ) (11) π J 2σ 2π where the unknown angular-momentum distribution has been approximated with a Gaussian distribution without dependence on the excitation energy and the two parities are assumed to be equally populated. J and σ correspond to the average value and the standard deviation o the spin distribution, respectively, and are ree parameters. The values we obtained or these ree parameters 21