Low-energy enhancement of M1 strength

Transkript

1 Text optional: Institutsname Prof Dr Hans Mustermann wwwfzdde Mitglied der Leibniz-Gemeinschaft Low-energy enhancement of M1 strength R Schwengner 1, S Frauendorf 2, A C Larsen 3 1 Institut für Strahlenphysik, Helmholtz-Zentrum Dresden-Rossendorf, Dresden, Germany 2 Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA 3 Department of Physics, University of Oslo, 0316 Oslo, Norway

2 Electromagnetic strength functions Electromagnetic strength functions (photon strength functions) describe average electromagnetic transitions strengths - in particular in the uasi-continuum of nuclear states at high excitation energy: f fil (E γ ) = Γ fil ρ(e i, J)/E 2L+1 γ Brink-Axel hypothesis: The strength function does not depend on the excitation energy The strength function for excitation is identical with the one for deexcitation Photoabsorption: f L = σ γ / [g (π hc) 2 E 2L 1 γ ]; g = (2J i +1)/(2J 0 +1)

3 Photonuclear and radiative-capture reactions Photonuclear reactions - fundamental processes to excite nuclear states with low spin Photon scattering or nuclear resonance fluorescence: Excitation of states up to the particle-separation energy in the (γ, γ ) process Photodissociation: Emission of particles in (γ,n), (γ,p), (γ, α) reactions Inverse reactions - radiative capture, (n,γ), (p,γ), (α, γ) Radiative neutron capture: important for the synthesis of heavy nuclei in stellar environments important for nuclear technologies (eg transmutation) Excitation of states at high energy and large level density so-called uasicontinuum of states Calculation of reaction rates using codes based on the statistical reaction model one important input: photon strength functions

4 Dipole strength in 94 Mo Dipole strength function f 1 = σ γ /[3(π hc) 2 E γ ] f 1 = Γ ρ(e x, J)/E 3 γ (γ, γ ) from 4 MeV to S n : G Rusev et al, PRC 79, (2009)

5 Dipole strength in 94 Mo Dipole strength function f 1 = σ γ /[3(π hc) 2 E γ ] f 1 = Γ ρ(e x, J)/E 3 γ (γ, γ ) up to 4 MeV: N Pietralla et al, PRL 83, 1303 (1999)

6 Dipole strength in 94 Mo ) -3 γ-ray strength function (MeV ( He, He ) Mo, Oslo data, E&B2009 norm 94 Mo(γ,x) E1 strength M1 strength Sum of E1 and M1 Dipole strength function f 1 = σ γ /[3(π hc) 2 E γ ] f 1 = Γ ρ(e x, J)/E 3 γ γ-ray energy E (MeV) γ 94 Mo( 3 He, 3 He ): M Guttormsen et al, PRC 71, (2005)

7 Dipole strength in 95 Mo Dipole strength function f 1 = σ γ /[3(π hc) 2 E γ ] f 1 = Γ ρ(e x, J)/E 3 γ 94 Mo(d,p) 95 Mo: M Wiedeking et al, PRL 108, (2012)

8 Experimental B(M1) and B(E1) values in nuclei around A = 90 B(M1) (µ N 2 ) < 88 = A < = 98 M1: 312 transitions E1: 171 transitions B(E1) (10 2 e 2 fm 2 ) E γ (kev) Data taken from NNDC data base:

9 Shell-model calculations around N = Mo/ 95 Mo/ 96 Mo: Z = g 9/2 protons, N = /3/4 1d 5/2 neutrons Shell-model calculations possible calculation of M1 transition strengths Up to now: Code RITSSCHIL used to describe M1 seuences at high spin in nuclides with N = 46 to 54 Present task: Calculation of B(M1) values of transitions between many states far from yrast, approaching the uasicontinuum Determination of average B(M1) values in energy bins Calculations for 94 Mo, 95 Mo, 96 Mo and for the Z = 40, N = 50 nuclide 90 Zr for comparison

10 Shell-model calculations around N = 50 Configuration space SM2: Two-body matrix elements: 0g 1p 1p 1/2 3/2 0f 5/2 π ν 0g 9/2 9/ Core Ni Code: RITSSCHIL 0g 7/2 1d 5/ ππ: empirical from fit to N=50 nuclei, 78 Ni core; X Ji, BH Wildenthal, PRC 37 (1988) 1256 πν, νν (0g 9/2,1p 1/2 ): emp from fit to N=48,49,50 nuclei, 88 Sr core; R Gross, A Frenkel, NPA 267 (1976) 85 πν (π0f 5/2,ν0g 9/2 ): experimental from transfer reactions; PC Li et al, NPA 469 (1987) 393 νν (0g 9/2,1d 5/2 ): exp from energies of the multiplet in 88 Sr; PC Li, WW Daehnick, NPA 462 (1987) 26 remaining: MSDI; K Muto et al, PLB 135 (1984) 349

11 Level energies in 90 Zr and 94 Mo Zr shell model SM Mo shell model SM2 11 π = + 11 π = E x (MeV) E x (MeV) J J

12 Average M1 strengths in 90 Zr and 94 Mo Zr shell model SM2 94 Mo shell model SM2 04 J = 0 i to 6 i, i = 1 to 40 J = 0 i to 6 i, i = 1 to 40 B(M1) (µ N 2 ) (π = +, transitions) (π =, transitions) B(M1) (µ N 2 ) (π = +, transitions) (π =, transitions) E γ (kev) E γ (kev) Enhancement of M1 strength toward very low transition energy Total M1 strength of transitions around 8 MeV in 90 Zr is in agreement with results of an experiment at HIγS [G Rusev et al, PRL 110, (2013)]

13 Average M1 strengths in 95 Mo and 94 Mo Mo shell model SM2 94 Mo shell model SM2 J = 1/2 i to 13/2 i, i = 1 to 40 J = 0 i to 6 i, i = 1 to 40 B(M1) (µ N 2 ) (π = +, transitions) (π =, transitions) B(M1) (µ N 2 ) (π = +, transitions) (π =, transitions) E γ (kev) E γ (kev) Average B(M1) values in bins of 100 kev of transition energy Enhancement of M1 strength toward very low transition energy in the two isotopes ν(1d 2 5/2 0g1 7/2 ) configuration preferred to ν(1d3 5/2 0g 1 9/2 0g1 7/2 ) configuration in 95 Mo

14 Average M1 strengths in 90 Zr and 94 Mo Zr shell model SM2 94 Mo shell model SM2 1 J = 0 i to 6 i, i = 1 to J = 0 i to 6 i, i = 1 to 40 B(M1) (µ N 2 ) (π = +, transitions) (π =, transitions) B(M1) (µ N 2 ) (π = +, transitions) (π =, transitions) E i (kev) E i (kev) Average B(M1) values in bins of 100 kev of excitation energy 90 Zr: Large peaks between about 59 and 75 MeV for π = arise from states dominated by the configuration π(1p 1 1/2 0g1 9/2 ) ν(0g 1 9/2 1d1 5/2 ) 94 Mo: Large peaks between about 15 and 30 MeV for π = + and π = arise from states dominated by the configurations π(0g 2 9/2 ) ν(1d2 5/2 ) and π(1p 1 1/2 0g3 9/2 ) ν(1d2 5/2 ), respectively

15 Average M1 strengths in 90 Zr and 94 Mo Zr shell model SM2 94 Mo shell model SM2 B(M1) (µ N 2 ) J = 0 i to 6 i, i = 1 to 40 (π = +, transitions) (π =, transitions) B(M1) (µ N 2 ) J = 0 i to 6 i, i = 1 to 40 (π = +, transitions) (π =, transitions) J i J i Average B(M1) values vs initial spin 94 Mo: Staggering of the values for π = + Large B(M1) values for transitions from states with the main configuration π(0g 2 9/2 ) ν(1d2 5/2 ) and even spins

16 Shell-model calculations for 94 Mo Configurations that generate large M1 transition strengths (active orbits with j π 0 and j ν 0): π = +: π(0g 2 9/2 ) ν(1d2 5/2 ) π = : π(1p 1 1/2 0g3 9/2 ) ν(1d2 5/2 ) π = +: π(0g 2 9/2 ) ν(1d1 5/2 0g1 7/2 ) π = : π(1p 1 1/2 0g3 9/2 ) ν(1d1 5/2 0g1 7/2 ) π = +: π(0g 2 9/2 ) ν(1d2 5/2 0g 1 9/2 0g1 7/2 ) π = : π(1p 1 1/2 0g3 9/2 ) ν(1d2 5/2 0g 1 9/2 0g1 7/2 ) π = +: ν(1d 2 5/2 0g 1 9/2 0g1 7/2 ) Mixed-symmetry and spin-flip configurations

17 Shell-model calculations for 90 Zr Configurations that generate large M1 transition strengths (active orbits with j π 0 and j ν 0): π = +: π(1p 2 1/2 0g2 9/2 ) ν(0g 1 9/2 1d1 5/2 ) π = : π(1p 1 1/2 0g1 9/2 ) ν(0g 1 9/2 1d1 5/2 ) π = +: π(1p 2 1/2 0g2 9/2 ) ν(0g 1 9/2 0g1 7/2 ) π = : π(1p 1 1/2 0g1 9/2 ) ν(0g 1 9/2 0g1 7/2 ) π = +: ν(0g 1 9/2 0g1 7/2 ) Mixed-symmetry and spin-flip configurations

18 M1 strength functions Calculation of the M1 strength function according to: f M1 (E γ ) = 16π/9 ( hc) 3 B(M1)(E γ ) ρ(e i, J) ρ(e i, J) - level density of the shell-model states Total level densities ρ(e i ) for E i < 3 MeV are well described by the constant-temperature expression: ρ(e i ) = ρ 0 exp(e i /T ρ ) with T ρ 06 MeV

19 M1 strength function in 94 Mo Mo f 1 (10 9 MeV 3 ) E1 (γ,n) data ( 3 He, 3 He ) data E γ (MeV)

20 M1 strength function in 94 Mo Mo M1 strength function f M1 (E γ ) = 16π/9 ( hc) 3 B(M1)(E γ ) ρ(e x, J) f 1 (10 9 MeV 3 ) E1 ( 3 He, 3 He ) data M1 shell model (γ,n) data ρ(e x, J) - level density of the shell-model states, includes π = +, π =, all spins from 0 to E γ (MeV) RS et al, PRL 111, (2013)

21 M1 strength function in 94 Mo Mo M1 strength function f M1 (E γ ) = 16π/9 ( hc) 3 B(M1)(E γ ) ρ(e x, J) f 1 (10 9 MeV 3 ) E1 + M1 E1 ( 3 He, 3 He ) data M1 shell model (γ,n) data ρ(e x, J) - level density of the shell-model states, includes π = +, π =, all spins from 0 to E γ (MeV) RS et al, PRL 111, (2013)

22 M1 strength functions in 95 Mo and 96 Mo Mo Mo 10 2 E1 + M E1 + M1 (γ,n) data f 1 (10 9 MeV 3 ) E1 M1 shell model ( 3 He, 3 He ) data f 1 (10 9 MeV 3 ) E1 ( 3 He, 3 He ) data M1 shell model E γ (MeV) E γ (MeV) RS et al, PRL 111, (2013)

23 Generation of large M1 strengths J + 1 J J π J ν J π M1 J ν µ = Z (g lπ lπ + g sπ s π ) + N (g lν lν + g sν s ν ) B(M1,J i J f ) = (2J i + 1) 1 f µ i 2

24 Generation of large M1 strengths J + 1 J J π J π J ν M1 J ν Configurations including protons and neutrons in specific high-j orbits with large magnetic moments Coherent superposition of proton and neutron contributions for specific combinations of g π and g ν factors and relative phases ( mixed symmetry ) Large M1 strengths appear between states with eual configurations by a recoupling of the proton and neutron spins

25 Generation of large M1 strengths Analogous shears mechanism in magnetic rotation S Frauendorf, Rev Mod Phys 73, 463 (2001) Examples near A = 90: 82 Rb, 84 Rb H Schnare et al, PRL 82, 4408 (1999) RS et al, PRC 66, (2002) B(M1) µ 2

26 Predicted Appearance of magnetic rotation Neutron Number N Proton Number Z j" 2 j S Frauendorf, Rev Mod Phys 73, 463 (2001)

27 Mo(n,γ) reaction rates with and without low-energy enhancement Mo (n,γ) rates, T =1, GLO const T 9 Low-energy exponential M1 GLO / N A σv 10 N A σv upm mass number A (target nucleus) Courtesy of AC Larsen

28 Summary Calculation of a large number of M1 transition strengths between the lowest 40 states each with spins 0 to 6 in 90 Zr, 94 Mo, 96 Mo and spins 1/2 to 13/2 in 95 Mo The calculations show an enhancement of the average B(M1) values toward very low transition energy A dipole strength function deduced from the average calculated B(M1) values in 94 Mo is in agreement with a strength function deduced from a ( 3 He, 3 He ) experiment Enhanced M1 strength at low energy is generated by transitions between closely lying states of all considered spins Large M1 strengths result from a recoupling of the spins of specific high-j proton and neutron orbits Large M1 strengths at about 8 MeV are generated by the spin-flip configuration ν(0g 1 9/2 0g1 7/2 ) The low-energy enhancement of dipole strength has drastic conseuences for stellar (n,γ) reaction rates of neutron-rich nuclides