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(1) NIC-IX Satellite WS Institut für Kernchemie, Univ. Mainz, Germany - HGF VISTARS, Germany - Department of Physics, Univ. of Notre Dame, USA Karl-Ludwig Kratz Gross –decay properties for astrophysical applications

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(2) NIC-IX Satellite WS 2006 Nuclear data in astrophysics What data are needed in nuclear astrophysics ? (A)Quiescent nucleosynthesis e.g. H-, He-burning; s-process nuclear masses (reaction Q-values) charged-particle reaction rates (e.g. (p, ), (, ), (,n)) neutron capture-rates nuclear structure properties (e.g. E sp, J, C 2 S) for 10s to 100s of isotopes NEAR -stability (B) Explosive nucleosynthesis e.g. rp-process, p-process; weak and main r-process nuclear-masses (Q, S p, S n ) half-lives (T 1/2,; g.s., isomers) -delayed quantities (P p, P n, P f ) neutron capture rates neutrino reactions nuclear-structure-properties (e.g. 2, E sp, J …) for 100s to 1000s of isotopes FAR-OFF -stability

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(3) NIC-IX Satellite WS 2006 What are the nuclear data needed for? as input for astrophysical calculations star evolution, chemical evolution of Galaxy, specific nucleosynthesis processes WARNING ! Nuclear data (n.d.) are only ONE set of input parameters among SEVERAL astrophysics parameter sets Depending on mentality of the star-couturier, nuclear data are considered unimportant astro-parameters dominate n.d. just telephone numbers (too) many (free) parameters n.d. effects invisible important nuclear and astro-parameters of equal standing n.d. to constrain astro-parameters learning nucl. structure from astro-observables mathematicalnuclear astrophysics

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(4) NIC-IX Satellite WS 2006 scaled theoretical solar r-process scaled solar r-process Nb Zr Y Sr Mo Ru Rh Pd Ag Ba La Ce Pr Nd Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Hf Os Ir Pt Au Pb Th U Ga Ge Cd Sn Elemental abundances in UMP halo stars r-process observables Solar system isotopic abundances, N r, FUN-anomalies in meteoritic samples isotopic composition Ca, Ti, Cr, Zr, Mo, Ru, Nd, Sm, Dy r-enhanced Historically, nuclear astrophysics has always been concerned with interpretation of the origin of the chemical elements from astrophysical and cosmochemical observations, description in terms of specific nucleosynthesis processes (already B²FH, 1957). [] ALLENDE INCLUSION EK Mass number CS abundances T 9 =1.35; n n = Basic astronomical question: r-process, Bi

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(5) NIC-IX Satellite WS 2006 Nuclear models to calculate T 1/2 and P n – (I) Theoretically, the two gross/ integral -decay quantities, T 1/2 and P n, are interrelated via their usual definiton in terms of the so-called -strength function [S (E)] What is that? … a natural adoption of the strength function concept employed in other areas of nuclear physics, e.g.: single-particle strength functions, s-, p-wave neutron strength functions, multipole strength functions for photons. S c = S c refers to the behavior of the squares of overlap integrals ( ² c ) between two sets of nuclear wave functions: l represents various states of excitation, classified by E, J, T; c refers to the different reaction / decay channels, classified by E part, l part,… is the density of levels.

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(6) NIC-IX Satellite WS Nuclear models to calculate T 1/2 and P n – (II) Application to -decay: Theoretical definition (Yamada & Takahashi, 1972) S = D -1 · M(E) ² · (E) [s -1 MeV -1 ] M(E) average -transition matrix element (E) level density D const., determines Fermi coupling constant g v ² Experimental definition (Duke et al., 1970) S (E) = b(E) f(Z, Q -E) · T 1/2 [s -1 MeV -1 ] b(E) absolute -feeding per MeV, f(Z, Q -E) Fermi function, T 1/2 decay half-life. T 1/2 as reciprocal ft-value per MeV T 1/2 = S (E i ) x f (Z,Q -E i ) 0 E i Q 1 1 f(Z, Q -E i ) (Q -E i ) 5 S (E) E*[MeV] Q Fermi function T 1/2 sensitive to lowest-lying resonances in S (E i ) P n sensitive to resonances in S (E i ) just beyond S n easily correct T 1/2 with wrong S (E) same T 1/2 ! x10 3 6x10 5

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(7) NIC-IX Satellite WS 2006 Nuclear models to calculate T 1/2 and P n – (III) Before any theoretical approach is applied, its significance and sophistication should be clear ! In general, 2 groups of models: (1)Models where the physical quantity of interest is given by a polynomial or some other algebraic expression. parameters adjusted to exp. data describes only a single nucl. property no nuclear wave functions no insight into underlying SP structure Examples: Kratz-Herrmann Formula (1973) Gross Theory (1973) · New exponential law for T 1/2 ( + ) (Zhang & Ren; 2006) T 1/2 ( - ) from GTGR + known log(ft)s (Kar, Chakravarti & Manfredi; 2006) · (2) Models that use an effective nuclear interaction and solve the microscopic, quantum-mechanical Schrödinger or Dirac equation. provides nuclear wave functions within the same framework, describes a number of nucl. properties (e.g. g.s.-shape; E sp, J, log(ft), T 1/2 … ) Examples: FRDM+QRPA (1997; 2006) Self-consist. Skyrme-HFB + QRPA (Engel et al.; 1999) Large-Scale Shell Model (Martinez-P. & Langanke; 1999, 2003) Density-Functional + Finite-Fermi System (Borzov et al.; 2003) PN-Relativistic QRPA (Niksic et al.; 2005)

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(8) NIC-IX Satellite WS 2006 Nuclear models to calculate T 1/2 and P n – (IV) (1)Simple statistical approaches assumptions: -decay energy is large (Q 5 MeV) high level density S (E) is a smooth function of E (e.g. S =const.; S (E)); is insensitive to nature of final states; does not vary significantly for different types of nuclei (ee, o-mass, oo). The Kratz-Herrmann Formula, applied to P n values P n = C E i Q S (E i ) x f (Z,Q -E i ) S n E i Q with S =const. P n a (Q – S n ) (Q – C) b a, b as free parameters, to be determined by a log-log fit to known P n -values C is a cut-off parameter ( pairing-gap in -decay daughter)

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(9) NIC-IX Satellite WS 2006 Nuclear models to calculate T 1/2 and P n – (V) From Pfeiffer, Kratz & Möller, Prog. Nuclear Energy 41 (2002) Parameters from fits to known P n -values Region Lin. regressionLeast-squares fit 29 Z Z Z 57 a [%] b r² a [%] b red. ² … as a kind of joke: T 1/2 a (Q -C) Lin. regressionLeast-squares fit a [ms] b r² a [ms] b red. ² 2.74E E E E dashed line full line Parameters from fit to known T 1/2 of n-rich nuclei -b

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(10) NIC-IX Satellite WS 2006 Nuclear models to calculate T 1/2 and P n – (VI) … NO joke ! in 2006, two examples for big steps BACKWARDS : (I)X. Zhang & Z. Ren; PRC73, New exponential law for + decay half-lives of nuclei far from -stable line …we have discovered a new exponential law for T 1/2 ( + )…as a function of neutron number… log 10 T 1/2 = a x N + b authors give fit parameters for a and b, for (I) different Z-regions (II) allowed + -decay (III) first-forbidden + -decay (IV) second-forbidden + -decay finally a simple and accurate formula emerges: log 10 T 1/2 = (c 1 Z + c 2 ) N + c 3 Z + c 4 (II)K. Kar, S. Chakravarti & V.R. Manfredi; arXiv: astro-ph/ v1 Beta-decay rates (115 < A < 140) for r-process nucleosynthesis … the x th re-invention of the Gross Theory ! … shell model results… indicate that the GT strength distribution.. can be taken as a Gaussian. …GT strength distributes among 3 different types of final states: (a)discrete low-lying states with known log fts; (b)discrete states above with unknown strengths; (c)a part of the GT giant resonance (GTGR). admitted problems: centroid of GTGR from Bertsch & Esbensen (1987) width of GTGR free parameter ! …useful to experimental physicists for analyzing + -decay data.

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(11) NIC-IX Satellite WS 2006 Nuclear models to calculate T 1/2 and P n – (VII) (2) QRPA – type, microscopic models Recent review by J. Engel; Proc. Workshop on The r-Process… ; Seattle (2004); World Scientific Among recent theoretical schemes… Some methods emphasize global applicability, others self-consistency, and still others the comprehensive inclusion of nuclear correlations. None of the methods includes all important correlations, however. (2.1) FRDM + QRPA Macroscopic-microscopic mass model FRDM; Schrödinger equation solved in QRPA: GT force with standard choice for GT interaction latest version includes ff-strength from Gross Theory. disadvantage: not self consistent advantages: global model for all shapes and types of nuclei; large model space V GT = GT : _ · + GT = 23 MeV/A (2.2) Self-consistent Skyrme-HFB + QRPA Skyrme interaction SKO reasonable reproduction of energies and strengths of GT resonances; strength of T=0 pairing adjusted to fit known T 1/2 disadvantages: only spherical shape; only GT; only -magic (N=50, 82, 128); Skyrme interaction not good enough to make…decisive improvement advantage:self-consistency T 1/2 shorter than those from FRDM + QRPA

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(12) NIC-IX Satellite WS 2006 Nuclear models to calculate T 1/2 and P n – (VIII) (2.3) Large-scale Shell Model shell-model code ANTOINE; restricted, but sufficiently large SP model space, with residual interaction split into: (I) monopole part (II) renormalized G-matrix component monopole interaction tuned to reproduce exp. spectra; admitted, that truncated space may still miss some correlations. disadvantages: only -magic nuclei (N=50, 82, 126); only GT-decay; only spherical. advantages: several essential correlations included; treatment of ee and odd- isotopes. T 1/2 even shorter than those of SC-HFB + QRPA (2.4) Density Functional HFB + QRPA density-functional / Greens-function-based model + finite-Fermi-systems theory; not quite selfconsistent, but with well-developed phenomenology. disadvantage: only spherical nuclei advantages: all types of nuclei (ee, o-mass, oo); includes ff-strength microscopically. T 1/2 (in particular with ff) short

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(13) NIC-IX Satellite WS 2006 Nuclear models to calculate T 1/2 and P n – (IX) (2.5) Fully consistent relativistic -QRPA use of new density-dependent interaction in relativistic Hartree-Bogoliubov calculations of g.s. and particle-hole channels; finite-range Gogny D1S interaction for T=1 pairing channel; inclusion of particle-particle interaction. disadvantages: only spherical ee nuclei; Ni half-lives overestimated by factor 10 (spherical QRPA normalized to deformed 66 Fe 40 …! ); … our model predicts that 132 Sn is stable against -decay… (exp.: T 1/2 =40 s ; Q =3.12 MeV). advantages: …theoretical T 1/2 reproduce the exp. data for Fe, Zn, Cd, and Te…; sufficiently large model space. Conclusions J. Engel … it is argued on the basis of a measurement of a strength distribution (i.e. N= Cd) that the transitions at N=82 calculated by the shell model, HFB + QRPA and Density-functional + FFS are too fast. …this will force the other groups to go back and examine their calculated strength distributions. P. Möller …there is no correct model in nuclear physics. Any modeling of nuclear-structure properties involves approximations … to obtain a formulation that can be solved…, but that retains the essential features of the true system.

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(14) NIC-IX Satellite WS 2006 The r-process waiting-point nucleus 130 Cd Q QP 4QP J =1 + { g 7/2, g 9/2 } SnSn T 1/2, Q, E(1 + ), I (1 + ), log ft obtain a physically consistent picture! free choice of combinations : low E(1 + ) with low Q high E(1 + ) with low Q low E(1 + ) with high Q high E(1 + ) with high Q T 1/2 (GT) 233 ms 1130 ms 76 ms 246 ms

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(15) NIC-IX Satellite WS 2006 Shape of N r, abundance peak rising wing 122
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(16) NIC-IX Satellite WS 2006 Reduction of the TBME (1+) by 800 keV OXBASH (B.A. Brown, Oct. 2003) In In In In (new) (old) Experimental Level systematics of the lowest 1 + state in neutron-rich even-mass In isotopes Configuration 3 + : d 3/2 g 9/2 Configuration 1 + : g 7/2 g 9/2 Configuration 1 - : h 11/2 g 9/ keV Dillmann et al., 2003

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(17) NIC-IX Satellite WS 2006 Beta-decay odd-mass, N=82 isotones 0 h 11/2 282 d 3/2 s 1/2 g 7/ /2 + 1/2 + 3/2 + 11/ % % % % % % % % % % 4.5 g 7/ S 1n =5.246MeV S 1n =3.98MeV S 1n =3.59MeV P n =4.4% P n =9.3% P 1n =29% P 2n = 2% P 1n =39% P 2n =11% P 3n = 4.5% P 1n =25% P 2n =45% P 3n =11% 131 Sn Cd Pd Ru Mo E*[MeV] SP states in N=81 isotones P 4n = 8.5% P 5n = 1% I log(ft) S 1n =2.84MeV S 1n =1.81MeV

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(18) NIC-IX Satellite WS 2006 Effects of N=82 shell quenching g 9/2 g i 13/2 i p 1/2 f 5/2 p 1/2 p 3/2 p f 7/2 f h 9/2 h 11/2 h g 7/2 g d 3/2 d s 1/2 s d 5/2 d g 9/2 g f 5/2 f p 1/2 p h 9/2 ;f 5/2 N/Z B. Pfeiffer et al., Acta Phys. Polon. B27 (1996) 100% 70% 40% 10% Strengthof 2 -Term Single – Neutron Energies ( Units of h 0 ) high-j orbitals (e.g. h 11/2 ) low-j orbitals (e.g. d 3/2 ) evtl. crossing of orbitals new magic numbers / shell gaps (e.g. 110 Zr 70, 170 Ce 112 ) change of T 1/2 ?

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(19) NIC-IX Satellite WS 2006 E*[MeV] h 11/2 d 3/2 g 7/2 131 Sn Cd Pd Ru Mo g 7/2 11/2 - 3/2 + d 3/ g 7/2 7/2 + g 7/2 319keV 643keV 1299keV 1.96MeV 912keV 684keV 379keV 199keV T 1/2 =157ms T 1/2 =41.4/48.4ms T 1/2 =14.4/17.3ms T 1/2 =4.6/6.15ms T 1/2 =2.0/2.85ms L 2 standard 10% red. 20% red.40% red.60% red. Possible effect of shell quenching Nilsson potential; gradual reduction of l 2 -term

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(20) NIC-IX Satellite WS Ag p 1/2 g 9/2 T 1/2 (m)=(158 60) ms T 1/2 (g)=(46 ) ms m Ag 82 g 9/2 p 1/2 129g Ag 82 Beta-decay of 129 Ag isomers Separation of isomers by fine-tuning of laser frequency p 1/2 g 9/2 30% 70% 158ms 46ms

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(21) NIC-IX Satellite WS 2006 Isotope Experiment QRPA(GT+ff)* ) T 1/2 ( g 9/2 ) T 1/2 ( p 1/2 ) T 1/2 (stellar) 131 In 280ms 350ms 300ms 157ms 477ms 253ms 129 Ag 46ms 158ms 80ms 43ms 140ms 72ms 127 Rh ms 25.4ms 17.7ms 125 Tc ms 4.45ms 4.5ms 123 Nb ms 1.91ms 1.98ms * ) Nuclear masses: ADMC,2003 & ETFSI-Q Terrestrial and stellar half-lives of odd-mass N=82 waiting-point isotopes

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(22) NIC-IX Satellite WS mainly resulting from new nuclear structure information: better understanding of formation and shape of, as well as r-process matter flow through the A 130 N r, peak no justification to question waiting-point concept (Langanke et al., PRL 83, 199; Nucl. Phys. News 10, 2000) no need to request sizeable effects from -induced reactions (Qian et al., PRC 55, 1997) Astrophysical consequences r-process abundances in the Solar System and in UMP Halo stars......are governed by nuclear structure! Nuclear masses from AMDC, 2003 ETFSI-Q Normalized to N r, ( 130 Te) short T 1/2 long T 1/2

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(23) NIC-IX Satellite WS 2006 Lets come back to global calculations of gross -decay properties… … only model that can calculate on a macroscopic-microscopic basis all types of nuclei (nearly) all nuclear shapes g.s. and odd-particle excited-states decays: mass models:FRDM (ADNDT 59, 1995) ETFSI-Q(PLB 387, 1996) QRPA model:pure GT (ADNDT 66, 1997) GT + ff (see above; URL: ADNDT, to be submitted; KCh Mainz Report (unpubl.), URL:

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(24) NIC-IX Satellite WS 2006 Typical example: note: effect on P n ! T 1/2 and P n calculations in 3 steps – (I) (1) FRDM /ETFSI-Q Q, S n, 2 Folded-Yukawa wave fcts. QRPA pure GT with input from mass model potential: Folded Yukawa Nilsson (different, ) Woods-Saxon pairing-model: Lipkin-Nogami BCS (2) as in (1) with empirical spreading of SP transition strength, as shown in experimental S (E) SnSn Q (3) as in (2) with addition of first-forbidden strength from Gross Theory

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(25) NIC-IX Satellite WS 2006 Another spherical case: note : effect on T 1/2 ! …and a typical deformed case: Note: low-lying GT-strength; ff-strength unimportant! T 1/2 and P n calculations in 3 steps – (II)

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(26) NIC-IX Satellite WS 2006 Total Error = 5.54 Total Error = 3.52 Total Error = 3.73 Total Error = 3.08 P n -Values Half-lives (P. Möller et al., PR C67, (2003 )) Experimental vs. theoretical -decay properties T 1/2, P n gross -strength properties from FRDM + QRPA Requests: (I) prediction / reproduction of correct experimental number (II) detailed nuclear-structure understanding full spectroscopy of key isotopes, like 80 Zn 50, 130 Cd 82. QRPA (GT) QRPA (GT+ff) QRPA (GT) QRPA (GT+ff)

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(27) NIC-IX Satellite WS 2006 T 1/2 : 3 r-matter flow too slow r-matter flow too fast Effects of T 1/2 on r-process matter flow Mass model: ETFSI-Q - all astro-parameters kept constant r-process model: waiting-point approximation T 1/2 x 3 T 1/2 (GT + ff)

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(28) NIC-IX Satellite WS 2006 Conclusion nuclear-physics data for explosive nucleosynthesis calculations still unsatisfactory ! better global models with sufficiently large SP model space, for all nuclear shapes (spherical, prolate, oblate, triaxial, tetrahedral,…) and all nuclear types (even-even, odd-particle, odd-odd) more measurements masses gross -decay properties level systematics full spectroscopy of selected key waiting-point isotopes Despite impressive experimental and theoretical progress, situation of

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