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RIA, Beta Decay and the R-Process

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RIA, Beta Decay and the R-Process Preliminaries So Far Future Beta Decay, the R Process, RIA J. Engel April 4, 2006 Preliminaries So Far Future 1 Beta Decay is Important, Hard 2 What’s Been Done So Far 3 Future Work Preliminaries So Far Future Beta-Decay Far From Stability is Important 126 Limits of nuclear existence Half-lives are particularly 82 important at the r-process r-process “ladders” (N=50, 82, 126) 50 protons 82 ry where abundances peak. These d 28 rp-process 20 ctional Theo half-lives determine the 50 t Mean Fiel 8 28 neutrons Density Fun r-process time scale. 2 20 Selfconsisten 2 8 A=10 A~60 A=12 But others are also important; 0Ñω Shell Towards a unified affect abundances between Ab initio Model description of the nucleus few-body peaks. calculations No-Core Shell Model G-matrix Yes, uncertainties in astrophysics dwarf those in nuclear physics, but we won’t really understand the nucleosynthesis until both are reduced. 5 Preliminaries So Far Future Calculating Beta Decay is Hard. (though it gets easier in neutron-rich nuclei). To calculate beta decay between two states, you need: an accurate value for the decay energy ∆E (since −5 T1/2 ∝ ∆E ) matrix elements of the GT operator ~στ− and (sometimes) “forbidden” operators ~r~στ− between the two states .[Most of the strength of is above threshold, btw]. So your nuclear structure model must do a good job with nuclear masses, spectra, and wave functions, and to simulate the r process it must do the job in almost all isotopes. Preliminaries So Far Future Usefulness of RIA-Lite RIA – 1+ ion yields for reacceleration Geesaman to RISAC Reacceleration covers most of the path except near N = 126. Theory — no matter how phenomenological — should take it from there. Preliminaries So Far Future Approaches Tried So Far 1 Macroscopic/Microscopic Mass Model + Schematic QRPA 2 Self-consistent Skyrme Mean-Field Theory (HFB) + QRPA∗ 3 Relativistic QRPA 4 Shell Model 5 Finite Fermi Systems Theory∗ . Wave functions in all these models lack correlations, something that is compensated for by renormalizing gA. Preliminaries So Far Future ÅÓÐ ÐÖ¸ º È«Ö¸ ú¹Äº ÃÖØÞ »ËÔÒ ÙÔ Ø Ð Ö¹ÔÖÓ ×× º º º ½½ Macro/Micro + SchematicȺ QRPA M¨oller, Pfeiffer, Kratz (2003) 104 β− 103 decay (Theory: GT) The only calculation applied 102 globally. 101 0 Masses through, e.g., 10 − 1 finite-range droplet model 10 − 2 10 Total Error = 3.73 for 184 nuclei, Tβ,exp < 1 s ,exp with shell corrections. β Total Error = 21.16 for 546 nuclei (13 clipped), Tβ < 1000 s − 3 ,exp T / 10 4 10 QRPA: V ≈ κ~στ− · ~στ+ ,calc − β 3 β decay (Theory: GT + ff) with κ ∝ 1/A. T 10 102 First-forbidden (in “gross 101 theory”) added to GT a 100 few years ago. Shortens − 1 half-lives some at N = 82, 10 − 2 10 Total Error = 3.08 for 184 nuclei, Tβ,exp < 1 s more at N = 126. Total Error = 4.82 for 546 nuclei, Tβ,exp < 1000 s − 10 3 − − − 10 3 10 2 10 1 100 101 102 103 Experimental β-Decay Half-life Tβ,exp (s) ½6 ÙÖ ÊØÓ Ó ØÓ ÜÔ ÖÑÒØÐ ¬ Ý Ð¹ÐÚ× ÓÖ ÖÓÑ Ç ØÓ Ø Ú×Ø ÒÓÛÒ Ò ÓÙÖ ÔÖÚÓÙ× Ò ÑÓ Ð׺ ÖÖÓÖ× ØÖ Ö ÑÒÝ ÑÓÖ Ô ÓÒØ× ØÒ ÓÖ ÐÖ ÖÖÓÖ׺ Ì× × ÒÓØ ×Ò Ò Ø ¬ÙÖ׸ ÓÖ ×ÑÐÐ ÖÖÓÖ× ÑÒÝ Ô ÓÒØ× Ö ×ÙÔ ÖÑÔ Ó× ÓÒ ÓÒ ÒÓØÖº ÌÓ ÓØÒ ÑÓÖ ÙÒÖ×ØÒÒ Ó Ø ÖÖÓÖ Ò Ø Û ØÖÓÖ Ô ÖÓÖÑ ÑÓÖ ØÐ ÒÐÝ×׺ ÇÒ ÓØÒ ÒÐÝÞ× Ø ÖÖÓÖ Ò Ý ×ØÙÝÒ ÖÓ ÓعÑÒ¹×ÕÙÖ ´ÖÑ×µ ÚØÓÒ¸ Ò Ø× ÛÓÙÐ Ò X ½ ¾ ¾ ´Ì Ì µ ´½¿µ ÖÑ× ¬ ; ¬ ;ÜÔ Ò i½ ÀÓÛÚÖ¸ Ò ÖÖÓÖ ÒÐÝ×× × ÙÒ×ÙØÐ Ö¸ ÓÖ ØÛÓ Ö×ÓÒ׺ Ö×ظ Ø ÕÙÒØØ× ×ØÙ Preliminaries So Far Future Self-Consistent Skyrme HFB + Canonical-Basis QRPA 25 90Zr 20 Just one calculation, in ladder nuclei, with ) 15 T no forbidden decay. G ( B Same energy-density functional in 10 HFB and QRPA, so that most 5 SkO' SLy5 SkP unknown physics is in functional. Expt 0 0 0 2 4 6 8 10 12 14 16 18 20 Skyrme functional SkO chosen excitation energy [MeV] because did best with GT distributions. 102 One free parameter: strength of 101 t 2 p / x 1 e T T = 0 pairing (it’s zero in schematic / c 0 2 l / a 10 1 c QRPA.) Adjusted in each of the T 10-1 three regions to reproduce measured 80Zn 78Zn 76Zn -2 lifetimes. 10 82Ge 0 50 100 150 200 250 300 350 V0 [MeV] Preliminaries So Far Future Half-lives at ladder nuclei are shorter than in global approach at N = 50 and 82 (even with forbidden contribution in global calculations), longer at N = 126. HFB+QRPA+SkO' HFB+QRPA+SkO', V0=0 102 FRDM+QRPA ETFSI+QRPA Expt. 101 ] s [ 0 2 / 10 1 T 10-1 10-2 N=50 N=82 N=126 10-3 20 22 24 26 28 30 32 38 40 42 44 46 48 60 62 64 66 68 70 Charge Number Z Preliminaries So Far Future Further Development of HFB+QRPA So far: Improving the isovector “T-odd” Energy Functional Z 3 E = (Heven + Hodd) d r 0 Hodd = Cs~s(~r) ·~s(~r) −→ g0 2 + C∆~s(~r) · ∇ ~s(~r) ~ 0 0 + CT~s(~r) · T (~r) −→ g0, g1 with ~s(~r) the spin density and T~ (~r) the “kinetic” spin density. [The g 0 are the nuclear-matter spin-isospin “Landau parameters”.] 0 Only enough data to determine one combination of parameters g0. Preliminaries So Far Future Preliminaries So Far Future Shell Model The best available approach, at present, if you have large model space, good effective interactions and transition operators, etc. Two calculations reported for N = 82, with no forbidden contributions. 0 10 SM ETFSI FRDM Martinez-Pinedo and HFB Expt. Langanke −1 10 B.A. Brown et al (s) 1/2 T 10−2 Half-lives in two calculations are similar, the first group’s even shorter than in 10−3 40 42 44 46 48 50 HFB+QRPA. Charge Number Z But extension to deformed nuclei still a long way off. Preliminaries So Far Future Finite Fermi Systems Theory A Green’s-function-based approximation to the self consistent HFB+ QRPA Like HFB+QRPA, FFST applied only in spherical nuclei, though approach is applicable generally. Currently includes forbidden transitions, which have moderate effect at N = 82, large effect at N = 126. Half-lives at N = 82 are between those of HFB+QRPA and shell model. Preliminaries So Far Future I. N. BORZOV PHYSICAL REVIEW C 67, 025802 ~2003! FIG. 5. The experimental b-decay half-lives for the N582 chain taken from the NUBASE compilation @57# compared to DF3 FIG. 6. The b-decay half-lives for the N5126 chain calculated (Q50.81, a: allowed transitions, a11 f : the ®rst-forbidden transi- with the DF3 (Q50.81, a: allowed transitions, a11 f : the ®rst- tion included!,HFB@22# (Q50.64) and shell-model results @3# 5 forbidden transition included! and with the shell-model @4# (Q 0.55). 5 (TSM , Q 0.55 was used!. Also shown are the half-lives against the 2 5 (ne ,e ) capture at the electron neutrino temperatures Tn 4MeV (T4) @20# and 8 MeV (T8) @60# calculated for Ln 4! shows that Coulomb decay mechanism dominates in these 51052 erg s21 and R5100 km. nuclei. The experimental evidence of the high-energy ®rst- forbidden transitions above 132Sn has long been known @59#. In the recent study @26#, the b-decay half-lives have been 138 be the last bound tin isotopes, it turns to be 170Sn within the measured up to Sn. Within the Qb window of 9.0 MeV, the experimental decay scheme for 135Sn demonstrates the MSk7. At the same time, the energy-dependent T-matrix in- 200 existence of low energy GT transitions at 4±5 MeV and of teraction leads to the neutron drip-line located above Sn high energy ®rst-forbidden transitions at 7±9 MeV @26#. The @36#. With the ``modi®ed'' neutron drip-line a role of forbid- total half-lives of 450~50! ms and 520~30! ms have been den decays may be more important, as the driving operators 135 reported in Ref. @26# for Sn in agreement with 0.6~0.1! s contain the factor r/R0. A possible existence of superallowed found earlier in Ref. @59#. Our estimate @23# was 2470 ms for Fermi, as well as accelerated Gamow-Teller and ®rst- the pure GT decay and 520 ms with ®rst-forbidden decays forbidden b decays may be anticipated in doubly-magic included. The present calculations give the half-life of 482 drip-line systems. Our RPA estimate of the half-life for 174Sn ms for 135Sn. is 0.58 ms for the pure GT decay and 0.18 ms with the ®rst In Fig. 5 we display the results of the DF3 calculations forbidden decays included. This subject deserves a further (Q50.81) of pure GT decays and including the ®rst- study. forbidden decays for nuclei at N582 and Z,50. The com- parison is made with the HFB results @22# obtained with the À Ä 8 C. b decay vs „ne ,e … capture in N 126 region same particle-particle interaction strength gj as in the present work and Q50.64. Also shown are the shell-model results In the important r-process region near Z'60±75 and N @3# and measured half-lives.
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