Direct and β-delayed multi-proton emission from atomic nuclei with a time projection chamber: the cases of 43 Cr, 45 Fe, and 51 Ni

Transcription

1 Eur. Phys. J. A () 8: 79 DOI./epja/i-79- Regular Article Experimental Physics THE EUROPEAN PHYSICAL JOURNAL A Direct and β-delayed multi-proton emission from atomic nuclei with a time projection chamber: the cases of Cr, Fe, and Ni L. Audirac,a, P. Ascher,b, B. Blank,c, C. Borcea, B.A. Brown, G. Canchel, C.E. Demonchy, F. de Oliveira Santos,C.Dossat, J. Giovinazzo,S.Grévy,d,L.Hay,e,J.Huikari, S. Leblanc, I. Matea, J.-L. Pedroza, L. Perrot, J. Pibernat, L. Serani,C.Stodel, and J.-C. Thomas Centre d Etudes Nucléaires de Bordeaux Gradignan, Université Bordeaux - UMR 797 CNRS/INP, Chemin du Solarium, BP, F-7 Gradignan Cedex, France National Institute for Physics and Nuclear Engineering, P.O. Box MG, Bucharest-Margurele, Romania Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 88-, USA Grand Accélérateur National d Ions Lourds, CEA/DSM-CNRS/INP, BP 7, F-7 Caen Cedex, France Institut de Physique Nucléaire, rue Georges Clémenceau, F-9 Orsay, France Received: 8 June / Revised: October Published online: December c Società Italiana di Fisica / Springer-Verlag Communicated by R. Krücken Abstract. The two-proton radioactivity of Fe was studied experimentally with a time projection chamber. The aim of the experiment was the reconstruction of the proton tracks in three dimensions. Energy and angular correlations have been determined and the data are compared with theoretical models, in particular with a three-body model. Moreover, the decay of Cr was studied and β-delayed one-, two- and threeproton emission could be established. The correlations observed for β-delayed two-proton emission favour a sequential emission. Finally, β-delayed two-proton emission was observed for the first time for Ni. Introduction Two-proton radioactivity was predicted in the beginning of the 9s by Goldansky [] for ground-state emitters like Fe. This exotic decay mode concerns proton-rich nuclei with an even number Z of protons for which pairing effects allow the simultaneous emission of two protons whereas their sequential emission is energetically forbidden. The observation of two-proton (p) radioactivity was achieved for the first time in for Fe [,]. During these experiments, the heavy ions were implanted in silicon detectors from which the two protons could not escape. Therefore, only the decay time and the total decay energy could be measured, associated with the absence of a Present address: CEA Saclay, DSM/Irfu/SPhN, Orme des Merisiers, F-99 Gif-sur-Yvette Cedex, France. b Present address: Max-Planck-Institut für Kernphysik, Saupfercheckweg, D-97 Heidelberg, Germany. c blank@cenbg.inp.fr d Permanent address: Centre d Etudes Nucléaires de Bordeaux Gradignan, Université Bordeaux - UMR 797 CNRS/ INP, Chemin du Solarium, BP, F-7 Gradignan Cedex, France. e Permanent address: Laboratoire PhLAM, Bât. P - USTL, F-Villeneuve d Ascq Cedex. β or γ emission, as expected for two-proton radioactivity. However, in order to study in detail the emission process, the observation of the two individual protons and the reconstruction of the tracks in the three-dimensional space is needed. Therefore, a Time Projection Chamber (TPC) was developed [] in order to measure the angular and energy correlations between protons needed for comparisons with theoretical models. First results from the present experiment which enabled us to visualise for the first time the two protons in the decay of Fe by two-proton radioactivity were published by Giovinazzo et al. []. High-statistics data for Fe with a time projection chamber which allowed for the first time a D reconstruction of the p events were obtained by Miernik et al. [,7]. In the first part of this article, we will present the experimental setup. Then, the analysis procedure will be described and, finally, the results will be presented. Especially, the characterization of the TPC will be exposed before showing the results concerning Fe, Cr, and Ni. Experimental setup The experiment was performed at the LISE separator of GANIL. The ions of interest were produced by fragmentation of a primary beam of 8 Ni + with an energy of

2 Page of Eur. Phys. J. A () 8: 79 ΔE (u.a.) 8 7 Cr Fe TOF (u.a.) Fig.. Example of an identification matrix where the energy loss in the first silicon detector is plotted as a function of the time of flight between a micro-channel plate and the silicon detector. The locations of the exotic nuclei Cr and Fe are indicated. Fig.. The photograph shows the different elements of the TPC: the beam entrance window, the electrodes for the electric field for the drift of the ionization electrons, and the GEMs to multiply the number of electrons which are collected on the detection plane. On the bottom, one can see part of the readout electronics. 7 MeV/nucleon and an average intensity of. μa ina nat Ni target ( μm). The ions were selected by means of their magnetic rigidity, their energy loss and their velocity with the LISE separator [8], consisting of two magnetic dipoles surrounding an achromatic energy degrader of beryllium followed by a Wien filter. The detection setup included two silicon detectors for the identification of the heavy ions by means of time-of-flight and energy loss measurements, micro-channel plate detectors for time-of-flight measurements and the TPC where the ions are implanted []. The principle of the time projection chamber is as follows: the heavy ions are implanted in the active volume of the TPC where the subsequent decay events occur. The active volume consists of a P gas mixture (% methane and 9% argon at mbar or mbar depending on the setting) which is ionized by the slowing down of the heavy ions and the decay protons. Due to an electric field, the electrons produced drift towards a set of four Gas Electron Multipliers (GEMs) [9] before being collected on a detection plane of two orthogonal sets of 78 strips []. Each strip gives information about the energy collected, yielding thus the projection of the tracks on the detection plane. The third dimension is given by the arrival time of the ionisation electrons. Figure shows a photograph of the different elements constituting the TPC. Analysis procedure Implantation events are distinguished from decay events by the presence of a signal in the silicon detectors in front of the TPC. The analysis procedure consists firstly in the identification of the heavy ions implanted in the detection setup. This is achieved by means of time-of-flight and energy loss measurements with the two silicon detectors. Figure shows an example of an identification matrix for Fe and Cr. The locations of the more exotic species are calculated by a polynomial extrapolation as a function of the charge Z and the third component of the isospin T z determined with fragments produced with high production rates. The data for Ni were acquired in an independent experiment optimized for Zn []. Details of the procedure can be found in ref. []. The second step of the procedure consists in correlating decay events to implantations of heavy ions. Each time an ion of interest is identified, a time correlation window is opened. The duration of this window is fixed at about four half-lives of the emitter considered. As a consequence, each decay event which occurs in this time window is correlated to the implanted isotope. Spatial correlations are used to reduce the number of wrong correlations. This is obtained by means of the energy spectra delivered by the TPC. The last step of the analysis procedure is the construction of the spectra delivered by the TPC. However, as each strip has its own gain for the energy and time channels, calibrations are needed to obtain spectra ready for the analysis (see ref. []). Analysis and results In this section, we will present the results obtained during the experiments. In a first part, a characterization of the TPC with the βp decay of Ni is presented. Then we will show the results concerning the two-proton decay of Fe and, finally, the β-delayed proton emission of Cr and Ni will be laid out.. Characterization of the detector with the βp emission of Ni Before analyzing two-proton decay events, a precise charaterization of the detector is needed allowing to develop the tools necessary for the treatment of two-particle events.

3 Eur. Phys. J. A () 8: 79 Page of x = (8. ±.) strips 8 y = (9. ±.) strips x d = (8. ±.9) strips x a = (. ±.) strips.. y = (9. ±.8) strips d y = (9.9 ±.) strips a. -. time signal (ns) Δt = (-9. ± 9.) ns time signal (ns) Δt = (-7. ± 8.) ns 8 Fig.. Complete analysis of an implantation event of Ni followed by the delayed emission of a proton. The left column represents signals for the X strips and the right column signals for the Y strips. The top row shows the implantation energy signal. The vertical lines represent the implantation position determined by the fit. On the central row, the correlated decay event is fitted. The solid vertical lines show the starting points of the proton track and the dashed lines its stopping points. The third row shows the time signal analysis of the decay event where the time data are fitted on different sections (see text for details). We use the βp decay of Ni for this purpose. As the energy deposited by the β particle emitted is not high enough for being detected, only the track of the proton is visible in the spectra. In ref. [], three proton energies are reported at.(),.() and.8() MeV with absolute intensities of.(),.(8) and.()%, respectively. The first two proton energies are interesting because they correspond approximately to the Q p value of Fe and the track lengths can be fully reconstructed within the active volume. Figure shows the analysis of an implantation event of Ni followed by a βp emission. The implantation signal is fitted by a Gaussian for the energy signal of the X strips (parallel to the beam axis) and by a folding of a Gaussian and a straight line for the energy signal of the Y strips (orthogonal to the beam axis). Note that the central strips are rejected for the strips parallel to the beam axis to exclude channels with saturation effects. This analysis gives the implantation positions of the heavy ions. The decay signal is adjusted at the same time for the X and Y strips by a folding of a Gaussian and a straight line, with the condition that the energy deposited on each dimension is the same. The fit function used is a good approximation of the Bragg curve corresponding to the energy loss of a charged particle in the gas. The result of the fit gives us the starting and stopping points of the proton track on each set of strips, the starting position corresponding to the ion implantation position. For the time analysis, taking into account the fact that the drift velocity of the electrons (.8() cm/μs in P at mbar and a field strength of V/cm) is constant inside the gas, a straight line is used to adjust the time spectra. However, as can be seen in fig., the time spectra show discontinuities along the trajectories. The origin of these problems is not completely understood, but it seems that they are correlated with the height of the energy signal. A procedure was developed to fit the time spectra on different sections with the same slope, but different offsets. The time analysis gives the drift-time difference between the starting and the stopping points of the track from the slope of the fit. We retain the time value for the strip set (X or Y ) where the projected track is the longest in order to reach the best precision.

4 Page of Eur. Phys. J. A () 8: 79 counts per mm E E =. MeV =. MeV Counts / 8 r (cm) Fig.. Track lengths in centimeters measured for βp decay events of Ni. The solid curve is a fit of the data with two Gaussians, the dashed and the dotted curves corresponding to the protons at. MeV and. MeV, respectively. The fitted range of the two proton groups is.8() cm and.() cm. These ranges have to be compared with the theoretical values [] of.9 cm and. cm. The events outside the Gaussians correspond to high-energy events which leave only part of their energy in the active volume of the TPC. The analysis of the decay events just laid out allows to test the capacity to reconstruct the track lengths from the energy and time analysis. Figure shows the distribution of track lengths calculated for all the βp decay events of Ni. The double structure observed can be fitted by two Gaussians the maxima of which correspond very well to the expected track lengths in P gas of protons of. MeV and. MeV as emitted by Ni. The relative branching ratio of the two proton groups emitted following the β decay of Ni as observed here is in fair agreement with the branching ratios determined by Dossat et al. [] (BR(. MeV) =.()%, BR(. MeV) =.(8)%), taking into account that the higher-energy protons have a higher probability to leave the active volume of the TPC. The proton group at.8 MeV does not form a peak in the figure as these protons do not deposit their full energy in the active volume of the chamber. This result shows the detector s capacity to reconstruct tracks of decay events provided that their track length is smaller than the dimensions of the chamber. Another way of testing the performances of the TPC is to determine the angular distribution of protons from Ni.Inthiscaseofaβ-delayed one-proton emitter, one expects an isotropic distribution. This is indeed the case, as shown in fig.. However, one observes also that events Theta ( ) Fig.. Angular distribution of the protons emitted from Ni. To generate this plot, only protons with a track length of less than cm were used to prevent protons from directly hitting the detection plane. are missing at very small and very large angles where the reconstruction of the angle has deficiencies. We did not explore this in more detail, because we believe that for the present statistics, this is without any importance.. Study of two-proton decay of Fe.. Global parameters The present experiment allowed for the first time the observation of two-proton decay events from Fe with an individual detection of the protons []. Ten decay events could be correlated in time and space to Fe implantation events. Seven of them are unambiguously identified as two-proton decay events. For the three other events, β- delayed proton emission is evidenced. One of these three events shows two tracks, the ranges of which are too long compared to the range of ground-state two-proton radioactivity events. This decay corresponds therefore to a βp decay event. For the two other events, no evidence of two tracks is visible. Therefore, we conclude that they are due to βp decays. Moreover, the total decay energy of these three events as measured with the GEMs is indeed lower than the energy deposited for two-proton radioactivity events. From these observations, we determine a branching ratio for two-proton radioactivity of , in nice agreement with the value of previous experiments of (. ±.) [] and (.7 ±.) [7] yielding a new average branching ratio of (.8 ±.). The time difference between an implantation and its subsequent decay event allows to determine the half-life of Fe. The corresponding spectrum is shown in fig.. However, we have to correct for the dead time of the DAQ of. ms. As this is a fixed dead time for each event, it shifts the total spectrum by the same amount. The experimental half-life was determined by means of the maximumlikelihood procedure and found to be T / = ms, in agreement with the average value from previous experiments of (. ±.) ms [] and (. ±.) ms [7] yielding

5 Eur. Phys. J. A () 8: 79 Page of counts / kev counts / ms =. T / +..8 ms decay time (ms)... E p = (. ±.) MeV GEM energy (kev) Fig.. Top: Decay time distribution obtained for the decay events of Fe. A half-life of ms is obtained. Bottom: Total decay energy spectrum as measured with one of the GEMs for two-proton radioactivity events of Fe.Adecayenergyof (. ±.) MeV is found. an average value of (. ±.) ms. With the branching ratio for p emission, we can determine the p partial half-life to be (.7 ±.) ms. The total decay energy for the two-proton radioactivity events can also be measured with the GEMs. Figure shows the energy spectrum of the corresponding events calibrated with a triple α source. An experimental decay energy of E p =(.±.) MeV is found, again in agreement with the average value from previous experiments of (.±.) MeV []. These results rely on a new analysis of the data already presented in ref. []... Correlation analysis We will focus now on the spectra of two-proton decay events delivered by the TPC. Their analysis will give the sharing of the total decay energy and the relative angle between the two protons. Figure 7 shows an example of a two-proton decay correlated to an implantation of Fe. The analysis of the implantation signal (top row) is described in sect... The sum of two foldings of a Gaussian and a straight line is used to adjust the decay energy spectra (second row). The X and Y strips are fitted at the same time to constrain the analysis and the energy deposited by each proton. The track of the two protons is clearly seen, which allows to determine their starting and stopping points. For the time spectra (third row), a straight line is used to adjust each part of the spectrum relative to each proton. We determine in this example that one proton is emitted upwards whereas the other is emitted downwards. This latter triggers all the time signal on the X strips. Therefore, the time signal of the proton going upwards is only seen on the Y strips,assoonasthe track of the first proton has stopped. The fit of the time signals is done on the whole range of the energy signals, except at the end of the trace where we remove five channels because the time distribution is no longer linear due to a small energy signal. Figure 8 shows the previous decay event reconstructed in the three-dimensional space and its projection on the detection plane which gives the energy deposited along the proton tracks. The previous analysis allows to study the correlations between protons. We will firstly interpret the energy correlations. The energy of each proton is determined by summing the signal of the strips belonging to the proton considered. Figure 9 shows the experimental histogram for the sharing of the decay energy between the two protons compared to the predictions of the three-body model [ 7] normalized to the experimental number of events. The three-body model is the only theoretical approach of twoproton radioactivity describing the dynamics between the two protons. The dynamics of the emission is treated by modeling the proton-core and the proton-proton interaction explicitly. The protons are taken to be on singleparticle levels. The experimental and the theoretical distributions are in nice agreement, showing that the two protons share equally the total decay energy, as expected for two-proton radioactivity in order to favour the barrier penetration. This result agrees with the findings of Miernik et al. [7]. To estimate the angle between the two protons, we need the third dimension which can be determined as described in the previous section for Ni. However, the track lengths for the two protons from Fe are much shorter than those of the protons from Ni. Therefore, the time

6 Page of Eur. Phys. J. A () 8: 79 x imp = (. ±.) strips 8 - y = (7. ±.) strips imp - - x = (. ± 7.) strips x = (. ±.) strips x = (. ±.) strips - - y = (9.7 ±.) strips y = (. ±.) strips y = (. ±.8) strips time signal (ns) Δt = (-8.9 ±.8) ns time signal (ns) Δt = (.9 ±.) ns 9 Fig. 7. Complete analysis of an implantation event of Fe followed by a two-proton emission. The left column represents signals for the X strips and the right column signal for the Y strips. Top: the analysis of the implantation spectra gives the implantation positions. Center: the correlated two-proton decay event is represented. The solid vertical lines show the starting points of the two protons. The individual tracks are represented by the dotted and dashed curves. The dotted and dashed vertical lines represent the stopping points of each track. Bottom: the time signal of the decay event and its analysis is shown. Refer to the text for more details. Z - 8 Fig. 8. Left: Reconstruction in three dimensions of the two-proton decay event shown in fig. 7. Right: Projection on the detection plane for this decay event. Color/grey levels indicate the energy deposited along the tracks. spectra are more difficult to fit. In order to circumvent this problem, we developed another procedure which allows to more reliably determine the third component of the tracks []. Firstly, the energy analysis laid out above gives the ratio of the total decay energy for each proton. With the precisely known total decay energy of.() MeV obtained in ref. [8], we can thus determine the energy of each proton. Secondly, the track length r of each proton under the present experimental conditions (gas nature and pressure) is calculated with an energy loss program []. Moreover, the energy analysis gives us the track lengths r p projected on the detection plane (X-Y plane). The range in the third dimension is now determined from the following equation: z = (r) (r p ). In this procedure, we need the time spectra only to decide whether a proton is

7 Eur. Phys. J. A () 8: 79 Page 7 of counts number.. exp. data exp. data + errors -body model -body model resolution In the following paragraph, we will compare our results with those of Miernik et al. [7] and theoretical predictions for the nuclear structure of Fe... Interpretation and comparison with model predictions E / E p (%) Fig. 9. Spectrum of the energy correlations between the two protons emitted by Fe. The dashed histogram shows the raw data, whereas the solid histogram shows the experimental data folded with error bars. The curve allows to compare the experimental data to predictions of the three-body model (taken from [] folded with the experimental resolution). counts number / exp. data exp. data + errors % p % p % p 8 8 ( ) D α r Fig.. Spectrum of the angular correlations between the two protons emitted by Fe. The solid histogram shows experimental data convoluted with error bars, whereas the dashed histogram shows the raw data. The curves allow to compare the experimental data to predictions of the three-body model of Grigorenko and co-workers for several p contributions [ 7]. emitted upwards or downwards in the TPC. Both methods are in agreement with each other for all events, which could be reconstructed by both methods. This latter method allows to reconstruct all the events in three dimensions. Figure shows the angular distribution obtained. The experimental distribution is compared with the predictions of the three-body model. Especially, the event at may signal the presence of a sizeable p orbital contribution in Fe. However, with only seven decay events, the conclusions have to be taken carefully. The three-body model of Grigorenko et al. [] predicts partial half-lives of.8 ms and 99. ms for pure p and f wave functions of Fe, respectively. We will use these partial half-lives and correct them with shell-model spectroscopic factors to determine a partial half-life for p emission from a combination of the two models, the three-body model and the shell model. This procedure is guided by the fact that the three-body model takes into account the emission dynamics, but is rather limited in the nuclear structure it considers, whereas the nuclear shell model describes nicely nuclear structure effects, but does not take into consideration the emission dynamics. Two-proton removal spectroscopic amplitudes (A) have been calculated using the SDPFU Hamiltonian [9]. The results in the LS coupling scheme for L = S =are A(f) =.9 for f and A(p) =.8 for p. Combining the half-lives calculated by the three-body model for pure configurations with the shell model spectroscopic factors, we obtain the shell model corrected partial halflives T c / (p) =.8ms/A (p) = ms and T c / (f) = 99 ms/a (f) = 9 ms. Unfortunately, the s contribution from the three-body model is not available to us. Nonetheless, we can go one step further and estimate the contribution from s twoproton decay. The nearest s orbit is the s / orbital from the filled sd shell. The pairing, J =, interaction will admix (n + )-particle two-hole components into the n- particle (proton) wave functions. In perturbation theory, the contribution to the spectroscopic amplitude is (s / ),J =,T = V (f 7/ ),J =,T = E[(n +)p h] E(np) For the interaction, we use the NLO nucleon-nucleon potential with the V lowk method for renormalizing the shortrange correlations and with core-polarization corrections up to hω. The value of the matrix element ranges from V =.7 MeV (without core-polarization) to.8 MeV (with core-polarization). The core-polarization is uncertain since it depends upon how one treats the model space and the energy denominators. The energy denominator is approximately the energy of the p-h pairing vibration in Ca. This state is fragmented over several components with T =, and [] with a centroid around MeV. For the present estimate we take V =. MeV. This gives a value of A(s) =.. For the two-proton decay lifetime we make a linear extrapolation in the log (T / ).

8 Page 8 of Eur. Phys. J. A () 8: 79 x = (8. ±.8) strips - - x = (7. ±.) strips 8 x = (. ±.) strips x = (8. ±.) strips x = (8. ±.) strips y = (97.8 ±.) strips y = (. ±.) strips 8 y = (8. ± 8.) strips y = (.8 ±.) strips y = (. ±.) strips Fig.. Top: analysis of a β-delayed proton emission event from Cr. Bottom: β-delayed two-proton emission from Cr. For an explanation of the different lines, see fig. 7. counts number exp. data simu. -% simu. -% counts number / exp. data isotropic emission 8 8 E / E p (%) 8 8 ( ) D α r Fig.. Left: Sharing of the total decay energy between the two protons emitted in the βp decay of Cr. The crosses show the experimental data. They are compared to simulations for an equal sharing (dashed histogram) and for a ratio of % % between the protons (solid histogram). The latter is in good agreement with the data, which favours a sequential emission of the protons. Right: Angular correlations between the two protons emitted in the βp decay of Cr. Experimental results are compared to a simulation of an isotropic emission (solid histogram). value of Grigorenko s results for p and f to obtain T / (s) =. ms. Thus T c / (s) =. ms/a (s) =.ms. The total half-life for two-proton emission is obtained by adding the three partial decay amplitudes coherently, /T /T c/ (spf) = c/ (s)+ /T/ c (p) + /T/ c (f), () to obtain T/ c (spf) =.7ms. This value is in good agreement with the average experimental partial half-life of Fe of.7() ms (present work and [,7]). From the above values, we can also derive the relative decay probability through the different configurations which are P (s )=(/.)/((/.)+(/)+(/9)) =.9, P (p )=., P (f )=.8. This means that to a large extent the decay strength goes through the (s) and (p) configurations of the wave function. The angular distribution of the two protons (fig. ) does not allow a detailed comparison with the three-body model. However, as in the case of Zn [], we will cut the spectrum in two, above and below, and integrate the experimental spectrum and the theoretical curves. From this procedure, we obtain a ratio R of the integral above over the total which varies as a function of the p contribution of the wave function. Comparing the experimental ratio to the theoretical ones, we determine an experimental p contribution of +77 %. This value can be compared to the decay probabilities determined in the preceeding paragraph and is in agreement with, although much less precise than, the result from Miernik et al. [] of ()%. As already mentioned, we find that relatively small admixtures of low-l amplitudes due to pairing can be important for two-proton decay. The estimates made in the s calculation need to be refined, and the method used

9 Eur. Phys. J. A () 8: 79 Page 9 of x imp = (9.9 ±.) strips 8 - y = (79.9 ±.) strips imp 7 - x = (. ±.) strips x = (. ±.9) strips x = (98.7 ±.7) strips x = (. ±.8) strips 7 - y = (. ±.9) strips y = (. ±.8) strips y = (. ±.) strips y = (.9 ±.) strips time signal (ns) time signal (ns) Δt = (-7. ± 9.) ns Δt = (. ± 7.8) ns Δt = (-. ±.) ns Fig.. Example of a βp decay event of Cr. The central line shows the tracks of three protons emitted after an implantation of Cr (top). They are fitted by the dash-dotted, dashed and dotted lines. The bottom row presents the time analysis for the Y strips where the trajectories are well defined. The first and third protons (dashed and dashed-dotted lines) leave the implantation point in opposite directions. Both of them are emitted towards the bottom of the active volume. The signal of the second proton (dotted line), which is emitted towards the top of the chamber, appears when the first proton has stopped. for the shell model amplitudes in two-proton decay needs to be connected more firmly with the two-proton decay reaction theory. In addition, our assumption that the various decay amplitudes are added coherently needs to be confirmed in terms of the two-proton decay models. If the rates are added incoherently then we would obtain T/ c (spf) =7.ms.. Study of β-delayed proton emission of Cr Our experiment allowed to study β-delayed proton emission of Cr. This nucleus was implanted in the TPC at the same time as Fe. As Cr is bound with respect to one- and two-proton emission, it can only decay by β decay possibly followed by the emission of one or several protons. Dossat et al. [] identified several peaks of β-delayed one-proton emission, and a possible β-delayed two-proton emission branch is mentioned with a total energy of (9) kev. Beta-delayed emission of one proton is confirmed in the present work. Figure shows one example of these events. Similarly, β-delayed two-proton emission is also clearly established. The analysis method used is described in the previous sections. An example of such a decay event is shown in fig.. About 8 events of β-delayed two-proton emission have been observed. Their analysis allows to study the sharing of the total energy between the two protons. The left part of fig. presents the experimental result. The two protons do not share equally the total energy. However, as the protons emitted in this decay mode have enough energy to leave the active volume of the TPC, limited by the drift cathode on the top, the drift electrodes on the sides and the first GEM on the bottom, simulations were performed taking into account different ratios of the decay energy sharing. Track lengths of protons are calculated by an energy loss program [] for a total energy of kev mentioned above. The modeling consists in simulating Bragg curves approximated by foldings of a Gaussian and a straight line on the X and Y strips. The energy deposited inside the active volume of the chamber is taken from the simulated curves. Results of simulations for equal sharing of the energy and for a ratio of % % of the total energy for each proton are compared to the data. A ratio of % % minimizes the difference with the experimental data. We conclude therefore that the two protons do not share equally the energy. This conclusion is in agreement with a sequential process for the β-delayed emission of the two protons via an intermediate state in the one-proton daughter nucleus, in contrast to two-proton radioactivity of Fe for

10 Page of Eur. Phys. J. A () 8: 79 Z Z Z - - Fig.. Reconstruction in the three-dimensional space of βp, βp and βp decay events of Cr, from top to bottom. The left column shows the tracks in the active volume of the chamber, whereas the projection on the detection plane of the decay events is shown on the right column. Grey/colour levels are indicative of the energy deposited along the tracks. which the protons share equally the decay energy and are emitted simultaneously. If we assume for the moment that the decay goes via one intermediate state in Ti, this energy sharing would correspond to a decay through a state either around. MeV or around. MeV in Ti. Although a few states are known at these high excitation energies, no assignment can be made. In addition, it is expected that the level density is quite high at 7 MeV excitation energy and that the decay is mediated by several intermediate levels in Ti. The signature of a sequential emission is also an isotropic distribution for the relative angle between the two protons. The experimental angles are shown in fig.. They are in agreement with an isotropic emission corresponding to a sinusoidal distribution. Therefore, we conclude that our results support a sequential emission of the protons via intermediate states in the nucleus Ti. For two events, we observe the emission of three protons after an implantation of Cr which signals β-delayed three-proton emission for this nucleus (see fig. ). The central pictures of the figure show the energy distribution on the X and Y strips clearly evidencing the emission of three protons spatially correlated to the implantation signal of Cr (top row). The Y strip time signal where three parts can be distinguished confirms the emission of three particles. Figure presents the spatial reconstruction (left column) of the processes of β-delayed emission of protons of Cr for the three events described above. The projection of the decay events on the detection plane (right column) shows the energy deposited along the tracks.

11 Eur. Phys. J. A () 8: 79 Page of - - Fig.. Beta-p emission from Ni. The figure shows two decay events observed after an implantation of a Ni ion as seen in the X- (left-hand side) and Y -plane (right-hand side), a clear indication for βp emission. Finally, relative branching ratios of the β-delayed emission of protons were calculated for the three processes. Relative branching ratios of (87. ±.)%, (.7 ±.)% and % are found, respectively, for βp, βp and βp emission. These results are in reasonable agreement with those presented in a recent publication []. With the total proton emission branching ratio of 9.()% [, ], we obtain average absolute branching ratios for βp, βp and βp emission of 79.()%,.()% and %, respectively, from our experiment.. Observation of β-delayed two-proton emission of Ni During the experiment devoted to the study of Zn [], Ni was continuously implanted in the TPC. Therefore, its decay could be studied at the same time. The reconstruction of the decay spectra allowed to observe for the first time a β-delayed p emission branch for this nucleus. Figure shows two examples of decays as seen in the X and Y detection planes. Due to a large number of implantations, we could also determine the branching ratio to be.()% for the β-delayed two-proton emission branch. The total proton emission branching ratio was determined in the work of Dossat et al. [] to be 87.(8)%. This weak βp emission branching ratio is in agreement with the expectations according to Detraz [] who predicted a βp/βp ratio of less than %. Conclusions We have presented the analysis of experimental data obtained with a time projection chamber which allowed to detect individually the protons emitted in the two-proton radioactivity of Fe. Despite the lack of statistics, the data show that the two protons share equally the total decay energy, as predicted for a simultaneous emission. Moreover, Cr was also produced during the experiment and its β-delayed emission of protons was analysed. βp emission is observed with an individual detection of the protons. A sequential emission is demonstrated from the energy sharing of the two protons and from the relative angle between them. We observed that Cr can emit up to three delayed protons and the branching ratios for βp, βp and βp emissions were extracted. Finally, we observed for the first time β-delayed twoproton emission from the ground state of Ni for which we determined the one- and two-proton branching ratios. We would like to thank the whole GANIL and, in particular, the LISE staff and the DAQ group for their support during the experiment. This work was supported by the Conseil Général d Aquitaine and by the NSF grant PHY-87. References. V.I. Goldansky, Nucl. Phys. 9, 8 (9).. J. Giovinazzo et al., Phys. Rev. Lett. 89, ().. M. Pfützner et al., Eur. Phys. J. A, 79 ().. B. Blank et al., Nucl. Instrum. Methods A, ().. J. Giovinazzo et al., Phys. Rev. Lett. 99, (7).. K. Miernik et al., Phys. Rev. Lett. 99, 9 (7). 7. K. Miernik et al., Eur. Phys. J. A, (9). 8. A.C. Mueller, R. Anne, Nucl. Instrum. Methods B, 9 (99). 9. F. Sauli, Nucl. Instrum. Methods A 8, (997).

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