Nuclear shell model studies of exotic nuclei and implications in astrophysics

Transcription

1 Nuclear shell model studies of exotic nuclei and imlications in astrohysics Yang Sun Shanghai Jiao Tong University KLFT-BLT Joint Worksho, Set. 7, 2011

2 Origin of heavy elements Based on USA National Academy of Science Reort Question 3 How were the elements from iron to uranium made?

3 Nuclei discussed in this talk

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5 CSRe: Cooling storage ring RBLL2+CSRe sochronous mass sectrometer 36 ArRB 78 KrRB End of 2007: test run End of 2008: 1st hysics run Fall of 2009: results

6 mortance of the Lanzhou mass measurement These short lived Z=N-1 and Z=N-2 masses have never been measured exerimentally. They lie near the roton dri-line and are very exotic nuclei. These masses so far have been calculated using the best knowledge in nuclear structure models. They can serve as a valuable testing ground. Masses of articular isotoes are those in connection to the even-even N=Z waiting oint nuclei, they are very imortant for nuclear astrohysical r rocess.

7 Mass measurement results Masses of these nuclei are measured for the first time. Current HRFL-CSR results have similar error bars as CDE redictions. t confirms that CDE method is reliable at least for 63 Ge, 67 Se. t shows some differences for 65 As and 71 Kr.

8 Coulomb dislacement energy (CDE) Difference in binding energy of mirror nuclei Binding energy of the roton-rich nucleus Binding energy of the neutron-rich nucleus D(A,T) calculated with Skyrme Hartreee-Fock method

9 Question of shae effect n these nuclei, different shaes are known to coexist near the ground state. Nuclear shae coexistence leads to shae isomeric states (excited states having relatively long lifetimes). eole then questioned the HF method of calculation of CDE.

10 Energies levels of 68 Se and 72 Kr Bouchez et al, RL (2003)

11 somer influence on abundances in X-ray burst t is ossible that a flow towards higher mass through the isomer branch can occur (calculations using multi-masszone x-ray burst model) Y. Sun, M. Wiescher, et al., Nucl. hys. A758 (2005) 765 Without any ossible isomer contribution Full flow through isomers rather than g.s.

12 吸积盘

13 r-rocess in x-ray burst Neutron star r-rocess = Raid roton cature rocess One of the major rocesses for heavy element roduction Most of the time is sent at the waiting oints

14 abundance slow b decay (waiting oint) Tc (43) Mo (42) Nb (41) Zr (40) Y (39) Sr (38) Rb (37) Sb (51) Sn (50) n (49) Cd (48) Ag (47) d (46) Rh (45) Ru (44) Kr (36) Br (35) 80 Se (34) 76 As (33) Ge (32) Ga (31) Te (52) Waiting oint nuclei Mass number

15 Abundance of x-ray burst ashes 1s 89% 90% of the reaction flow asses through 64 Ge via roton cature indicating that: 64 Ge is not a significant r-rocess waiting oint.

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18 mortant factors for a nuclear structure model Single article states (mean field art) Reflect shell structure (sherical, deformed) Adjust to exeriment Two-body interactions (residual art) Mix configurations (do not have in mean field models) Transition robabilities are sensitive test Model sace (configurations) Large enough to cover imortant arts of hysics f not ossible, introduce effective arameters

19 Nuclear structure models Shell-model diagonalization method Most fundamental, quantum mechanical Growing comuter ower hels extending alications A single configuration contains no hysics Huge basis dimension required, severe limit in alications Mean-field method Alicable to any size of systems Fruitful hysics around minima of energy surfaces No configuration mixing States with broken symmetry, cannot be used to calculate electromagnetic transitions and decay rates

20 Bridge between shell-model and mean-field method rojected shell model Use more hysical states (e.g. solutions of a deformed meanfield) and angular momentum rojection technique to build shell model basis erform configuration mixing (a shell-model concet) K. Hara, Y. Sun, nt. J. Mod. hys. E 4 (1995) 637 The method works in between conventional shell model and mean field method, hoefully take the advantages of both

21 General structure features for neutron-rich Cr and Fe nuclei largest deformation at N=38 or 40, mid-shell effect Smallest 2 + excitation, strongest B(E2) Ni, Zn, Ge isotoes do not show similar trend mortant neutron g 9/2 hysics Back-bending along Yrast line Negative-arity bands =9/2 band in odd-mass isotoes Softness near ground state No well-defined shae in ground state ossibility of rolate-oblate shae cometition near ground state Shae stabilized when nuclei rotate (~6)

22 Neutron-rich Fe isotoes: rojected shell model calculations Sun et al., hys. Rev. C80 (2009)

23 Rotational roerties of neutronrich Fe isotoes Comarison of calculated moments of inertia with data rregularity at ~ 8: alignment of g 9/2 neutrons at ~ 16: alignment of f 7/2 rotons

24 Negative-arity states in neutronrich Fe isotoes Large-scale shell model with only f shell sace cannot describe small E(2 + ) energy near N=40. rojected shell model including the neutron g 9/2 orbit describes the data correctly.

25 Wavefunctions with and without g 9/2 orbit? Shell models in smaller bases may reroduce energy levels, but the wave functions (B(E2) s) can be wrong. Y. Sun et al., hys. Rev. C 80, (2009). J. Ljungvall et al., hys. Rev. C 81, (R) (2010). B(E2,2-->0)=214(26) e 2 fm 4 for N=36 B(E2,2-->0)=470 (210) e 2 fm 4 for N=38

26 The role of neutron g 9/2 intruder The best lace to study the role of neutron g 9/2 orbit is from = 9/2 + state (band) in odd-neutron nuclei R. Ferrer et al. RC 81, (2010)

27 Exlore the nature of 9/2 + band Does the observed 9/2 + isomer in odd-mass Fe and Cr nuclei have a K = 9/2 comonent of neutron g 9/2 state with rolate deformation? Not ossible Or a K = 9/2 comonent of neutron g 9/2 state with oblate deformation? ( 59 Cr) Deacon et al., hys. Lett. B 622 (2005) 151

28 ossible shae of 9/2 + band Y.-C. Yang, H. Jin, Y. Sun, K. Kaneko, hys. Lett. B700 (2011) 44

29 Nature of 9/2 + band in odd-mass Cr and Fe isotoes SM calculation shows it has a rolate deformation, mainly of K=1/2 comonent of neutron g 9/2 state An intruder large j orbit with small K comonent (K=1/2) is a strongly decouled state which shows decouling effect Bandhead has a larger Low-sin members lie higher Only a favored branch is observed

30 Comarison of 9/2 + band in 59 Cr with rolate and oblate deformation

31 Sherical shell model calculations Magic nature of 132 Sn has recently been confirmed by Jones et al. Nature 465 (2010) 454. Sectroscoy of valence nuclei with one article in emty shells or one hole in comletely filled shells rovides direct information on single-article structure. Sectroscoy of nuclei with two articles or two holes rovides information on correlations between different kinds of airs.

32 revious shell model studies Sectra consist of two grous of excitations: Excitations of ure valence single articles (lower energy) Excitations of valence single articles couled with core excitation (higher energy) Calculations of simle shell models Lower energy sectra calculated by shell models with effective interaction of CD Bonn otential (the Oslo grou, M. Hjorth-Jensen et al. the taly grou, A. Covello et al. the MSU grou, A. Brown et al.) Higher energy sectra described by emirical interactions (J. Blomqvist et al.)

33 Our shell model calculation Shell model sace: Hamiltonian: Extended airing lus quadruole-quadruole with monoole corrections arameters: exerimental single-article states 5 x 3 =15 two-body arameters 6 monoole corrections

34 Shell model calculation considering article-hole excitations show features suorting magnetic rotation bands.

35 Summary The first mass exeriment at Lanzhou CSRe successfully measured several short lived Z=N-1 and Z=N-2 nuclei near the roton dri-line. The measured masses test existing nuclear structure models that calculate nuclear masses. Using the new mass of 65 As, 64 Ge is suggested not to be a significant waiting oint nucleus. rojected shell model describes the large deformation region of neutron-rich Cr and Fe nuclei with N~40. Large-scale sherical shell model with neutron core excitation describes nuclei beyond 132 Sn.

36 Model sace constructed by angular-momentum rojected states Wavefunction: M f MK with a.-m.-rojector: MK 2 1 d DMK D 2 8 Eigenvalue equation: ' H ' EN ' f ' 0 with matrix elements: H ' H KK ' ' N ' KK ' ' Hamiltonian is diagonalized in the rojected basis MK

37 Hamiltonian and single article sace The Hamiltonian H nteraction strengths c is related to deformation e by G M is fitted by reroducing moments of inertia G Q is assumed to be roortional to G M with a ratio ~ 0.15 Single article sace Three major shells for neutrons or rotons For very heavy nuclei, N = 5, 6, 7 for neutrons N = 4, 5, 6 for rotons H 0 c 2 c Q Q n G 2 / 3 M G e Q Q0 n Q0

38 Building blocks: a.-m.-rojected multi-quasi-article states Even-even nuclei: Odd-odd nuclei: Odd-neutron nuclei: Odd-roton nuclei:, 0 ˆ, 0 ˆ, 0 ˆ, 0 ˆ MK MK MK MK, 0 ˆ, 0 ˆ, 0 ˆ, 0 ˆ MK MK MK MK, 0 ˆ, 0 ˆ, 0 ˆ MK MK MK, 0 ˆ, 0 ˆ, 0 ˆ MK MK MK