Microscopic nuclear form factor for the Pygmy Dipole Resonance

Transcription

1

2 Microscopic nuclear form factor for the Pygmy Dipole Resonance M.V. Andrés - Departamento de FAMN, Universidad de Sevilla, Spain F. Catara - INFN-Sezione di Catania, Italy A. Vitturi - Dipartimento di Fisica, Università di Padova and INFN-Padova, Italy E. G. L.- INFN-Sezione di Catania, Italy

3 Experimental data Experimentally they have been measured mainly by mean of Coulomb excitation by various groups Experimentally they have been measured mainly by mean of ABOVE NEUTRON SEPARATION THRESHOLD Coulomb excitation by various groups exotic nuclei ABOVE NEUTRON SEPARATION THRESHOLD using the FRS-LAND setup at GSI using the RISING setup at GSI (for exotic nuclei Ni) P.Adrich et al. PRL 95 (5) 1351 O.Wieland et al. PRL 1 (9) 95 using the FRS-LAND setup at GSI using the RISING setup at GSI (for Ni) P.Adrich et al. PRL 95 (5) 1351 O.Wieland et al. PRL 1 (9) 95 BELOW NEUTRON SEPARATION THRESHOLD stable nuclei BELOW NEUTRON SEPARATION THRESHOLD stable nuclei with (, ) studies (Darmstadt with (, ) at KVI. with (17O,17O ) at LNL University) with (, ) studies (Darmstadt with (, ) at KVI. with (17O,17O ) at LNL D.Savran et al. PRL 1 (8) 351 University) D.Savran et al. PRL 1 (8) 351 J.Endres et al. PRC 8 (9) 343 J.Endres et al. PRC 8 (9) 343 F.C.L.Crespi et al. PRL113(14)151 F.C.L.Crespi et al. PRL113(14)151 D. Savran et al., PRL 97 (6)175 J. Endres et al., PRC 8 (9) 343 J. Enders et al., PRL 15 (1) 153 F.C.L. Crespi et al. PRL 113 (14) N. Paar, D. Vretenar, E. Khan and G. IS-E1 QPM 15 (c) (a).6 Bis(E1) [e fm ] Sn(, ) Sn(, ) 16 (b) Energy [MeV] FIG. (color online). 8 IS-E1 RQTBA (e) Colo`, Rep. Prog. Phys. 7, 691 (7) D. Savran, T. Aumann and A. Zilges, Prog. Bem(E1) [1 e fm ] see also D. Negi talk on Tuesday.8 Eα=136 MeV. -3 with (, ) at KVI. with (17O, 17O ) at LNL B(E1) [1 e fm ] Splitting of the low-lying dipole strength d / d [mb/sr] 14 week ending 19 NOVEMBER 1 PHYSICAL REVIEW LETTERS PRL 15, 153 (1) Part. Nucl. Phys. 7, 1 (13). 1 1 EM-E1 QPM A. Bracco, F.C.L. Crespi and E.G. Lanza, (f) 3 4 EM-E1 RQTBA 3 (d) Eur. A 51, Energy [MeV]Phys. J. Energy [MeV] 99 (15) (a) Singles cross section for the excitation of the J # ¼ 1! states in 14 Sn obtained in the (", "!) coincidence

4 Outline Pygmy Dipole Resonance (PDR) can be studied with isoscalar probe, in this case the radial form factors used in the cross section calculations play an important role. Form factors calculated within a microscopic model are compared with those provided by different macroscopic collective models. Their differences, in the shape and magnitude, are reflected on the calculated cross section and therefore jeopardize the extracted physical quantities.

5 O (IV ) 1M =Z A NX n=1 RPA calculations with SGII interaction r n Y 1M (ˆr n ) N A ZX r p Y 1M (ˆr p ) p=1 O (IS) 1M = A X i=1 (r 3 i 5 3 <r >r i )Y 1M (ˆr i ) db(e1) /de (e fm MeV -1 ) db(e1) /de (1 e fm 6 MeV -1 ) (b) (a) 56 Ni N=Z IVGDR isovector ISGDR isoscalar E(MeV) Dipole states db(e1) /de (e fm MeV -1 ) db(e1) /de (1 e fm 6 MeV -1 ) (b) (a) Ni N>Z isovector isoscalar E(MeV)

6 r x δρ (fm -1 ) = r x δρ (fm -1 ) ph PDR p n () j p +l p + 1 PDR IS IV ˆ j p ˆ ˆ j h [ X ph Y ] ph R l p j p (r) R lh j h (r) IVGDR ISGDR < j h 1 j p 1 >( + l p + l h,even) IVGDR ISGDR db(e1) /de (e fm MeV -1 ) db(e1) /de (1 e fm 6 MeV -1 ) (b) (a) PDR Ni N>Z IVGDR isovector ISGDR isoscalar E(MeV) This is a 3 nuclear transitions generated by the second order ΔL=1 transition operator and it can be seen as a compressional mode.

7 It is well established that the low-lying dipole states (the Pygmy Dipole Resonance) have a strong isoscalar component. Then these states can be studied and have been studied also with reactions where the nuclear part of the interaction is involved. In the experimental analysis, for these cases, a fundamental role is played by the radial form factors used

8 The description of inelastic cross section with isoscalar probes - DWBA, first order theory - Coupled Channel, high order effect important - Semiclassical approximations Example: the transition amplitude for the DWBA Z T DWBA = ( ) (k,r)f(r) (+) (k,r)dr the radial form factor F(r) contains all the structure effects, they can be derived in macroscopic or microscopic approaches F C (r) p B(EL) F N du N (r) (r) N r L+1 dr

9 Dipole radial form factors calculation Goldhaber-Teller for the IVGDR Harakeh-Dieperink for the ISGDR Microscopic form factor (double folding)

10 U ( r ) = Double folding potential r r = 1 A ( r 1 ) v (r 1 ) a ( r ) dr 1 d v nucleon-nucleon potential r + r r 1 Double Folding procedure r r 1! 1! r! r A! α! a! The nuclear form factors F (r )= RR [ An (r 1 )+ Ap (r 1 )] v (r 1 )[ an (r )+ ap (r )]r 1dr 1 r dr The transition densities δρ can be calculated in a macroscopic or microscopic way

11 T. J. Deal, NPA 17 (1973) 1; M. N. Harakeh and A. E. L. Dieperink PRC 3 (1981) 39 Macroscopic transition density for the ISGDR 1 = 1 (r) = 6 ~ mae x 1 R p 1r +(3r <r >) d dr ) (r) R 11 <r 4 > 5 3 <r > R is the half-density radius of the mass distribution. r x δρ (fm -1 ) RPA HD Ni. a) PDR b) ISGDR RPA HD For both states, the macroscopic transition density has been scaled according to the following condition Z 1 Z 1 1 RP A(r) r 5 dr = 1 macro(r) r 5 dr

12 (r) = p (r) + n C (r) + n S (r) x S = x Z + N C A ; x C = x N S A n = p = N S A N S A d dr C n Z + N C A d dr p d dr S n = N S isosc A d dr C + n p ( ) Z + N C A d dr S n = N S isov A d dr C n p ( ) Z + N C A d dr S n

13 . Ni.1 r x δρ (fm -1 ) p MPM n MPM p RPA n RPA

14 We compare the RPA isoscalar transition densities with the two macroscopic model. Ni.. a) PDR (isoscalar) b) PDR (isovector) r x δρ (fm -1 ) RPA HD MPM RPA MPM In both the macroscopic transition densities, the RPA ground state density has been used.

15 F (r) (MeV) RPA HD MPM PDR Ni + 1 C ISGDR E.G. Lanza, A. Vitturi and M.V. Andrés, PRC 91, 5467 (15) The form factors have been obtained with the double folding procedure with the M3Y nucleon-nucleon potential and with the micro (RPA) and macro transition densities Ni MeV/u DWBA calculations done with the DWUCK4 code dσ/dω (mb/sr) calcolo con pot. WS fitting folding e ff micros PDR RPA HD MPM calcolo con pot. WS fitting folding e ff micros ISGDR 1-6 a) b) θ c.m. (deg) θ c.m. (deg)

16 used for every inelastic scattering cross section F.C.L. ettheal., ed afterwards. Fig. 4Crespi (top panel) shows data d for the elastic scattering divided by the Ruther113 oss PRL section. The optical(14) parameter of the151 Woodspotentials that best fitted our data were, for the f the real and imaginary potential, V=5. MeV =3. MeV and for the radii and the di usethe real and imaginary parts rv =rw =1.16 fm and.67 fm, respectively. The Coulomb radius pawas rc =1. fm. To check the reliability and the y of our calculations, a comparison between the Using TRACE mental and the calculated cross sections for dif+ excited states was evaluated. The calculations prototype and excited states used the standard collective-model ctor, namely a deformed Woods-Saxon potenagata Demonstrator ployed in the FRESCO code. For the excited alculations the known B(E )" values [1, ] system sed. The central and bottom panels of Fig. 4 5 e experimental di erential cross sections for the on of the collective + states of 14 Sn at 1.13 nd 3.14 MeV, respectively, in comparison with culations. These predictions were obtained aspure isoscalar excitation implying that the ratio eutron matrix element Mn and proton matrix elm p is given by Mn /M p = N/Z. It is clear from this hat the calculated curves are in excellent agreeith the data, and support the interpretation of a oscalar nature of these transitions. DWBA analysis of the E1 states is presented in om panel of Fig. 5. Since the statistics were innt to get an angular distribution of the scattered of each separate state, the data were integrated xcitation energy region MeV. The crosscalculations for the Coulomb excitation (very to the total excitation using for the nuclear part ndard collective model form factor [1]) in the between MeV are shown with the dashed comparison with the data (bottom panel of Fig. used value for the summed B(E1) was. W.u. ar from this comparison that the cross sections ed to a pure Coulomb excitation (dashed line) Pb( O, Oγ) for example, the GDR), is shown as a black solid line in Fig. As one can see, this calculation accounts only for a rathe F.C.L. Crespi et al., small fraction of the measured yield. In this calculation th Coulomb part is the dominant one and it is fixed by the know PRC 91 (15) B(E1) value deduced from the (γ,γ433 ) data of Ref. [17 It is clear that the nuclear part is not well described by th standard distorted potential approach in9 the case of this 1 9Zr( 17O, 17O ) Zr of 1 state state. Similarly to what was done in recent analyses in 8 Pb [14] and 14 Sn [15], also for the 1 state at 6.44 Me in 9 Zr a calculation performedmev using a microscopicall atwas34 γ Pb at 34 MeV Figure 5: Top panel: Form factor associated to the PDR states for the 14 Sn+17 O system. The Coulomb and the nuclear components are shown together with the total one (solid black line). Bottom panel: di erential cross sections for the 1 states between MeV. The blue dashed line shows the DWBA calculations with the only Coulomb contribution while the red solid line represent the total. L. Pellegri et al., PLB 738 (14) 519 γ)14sn 14Sn(17O,17O at 34 MeV

17 Summary For the study of the Pygmy Dipole Resonance with isoscalar probe, the form factors calculated within a microscopic model are compared with those provided by different macroscopic collective models. Their differences, shown in the shape and magnitude, are reflected on the calculated cross section and therefore jeopardize the extracted physical quantities. For the PDR states, it is of paramount importance the use of a microscopic radial form factor

18 the PDR state can be better carried out at low incident energy (below 5 MeV/nucleon) using for instance Ni on Experiment with CHIMERA 1 C. In figure 3 the results for the nuclear and Coulomb contributions as well as the total one are shown for this at LNS (end of November) case for three different incident energies (1,, 3 Fig.%3%cross%section%for%PIGMY%resonance% A MeV). In frame b) the Coulomb cross section shows how At LNS a excitation%at%1,%,%3%mev/a primary 7Zn beam of 4 MeV/A on a 9Be target produce a secondary the low incident energy inhibits the excitation of the GDR Ni beam in the CHIMERA hall. A yield withof respect to thewas low lying states. Thisfor is due to the khz measured this beam. well known adiabatic cut-off effect that governs the 1 transition amplitudes for Coulomb excitation. Ni + We C would like to stress that, although the Coulomb 8 contribution for the PDR is very small, a constructive 3 MeV/nucleon (a) 1 MeV/nucleon interference is clearly shown 6in the lower frame where 1 MeV/nucleon the total contributions are plotted. At LNS the Ni Nuclear 4 beam was recently produced during a test experiment! in the CHIMERA hall, ( see fig.4). A yield of khz was measured for this beam. We propose therefore to (b) A MeV on a Coulomb use this beam at energy around 3 thick 6 1 C target (1 m) to excite the pigmy resonance. The!decay of the resonance can4be measured using the CsI(Tl) of the CHIMERA detector [chim]. The detection efficiency of such detectors to simulations, is of the rays, as evaluated with GEANT (c) Total order of 3% around 1 MeV6( integrating the energy released from 8 to 1 MeV ). Detection efficiency and We propose to use this beam at energy around 3 4 spectra quality was recently proved measuring the -decay of various 1C levels excited with proton beams A MeV on a thick 1C target to excite the pygmy Ni + C 3 A MeV resonance. The γ-decay of the resonance can be Fig.4%Identification%scatter%plot%of% Ni%fragmentation% beam measured using the CsI of the CHIMERA detector. dσ/de E (MeV) 5

19 Thank you for your attention