Modification of the Brink-Axel hypothesis for high-temperature nuclear weak interactions

Misch, G. Wendell; Fuller, George M.; Brown, B. A.

doi:10.1103/physrevc.90.065808

Cited by 40 publications

(46 citation statements)

References 56 publications

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“…The general Brink-Axel hypothesis [8][9][10] assumes that the strength distribution of transitions from any parent state is approximately the same, thus as a result E centroid (E i ) is independent on E i . Though it seems this hypothesis needs to be modified for E1 [11][12][13], M1 [14][15][16] (the low-energy γ anomaly) and GT [17] transitions, it is still being widely used to calculate neutron-capture rates [18], extract nuclear level densities [1,19,20] and can have a substantial impact on astrophysical relevance [2,21]. Sum rules are appealing not only because they characterize strength functions, but also because using closure some sum rules can be rewritten as expectation values of operators [22].…”

Section: Introductionmentioning

confidence: 99%

Transition sum rules in the shell model

Lü

Johnson

2018

Phys. Rev. C

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An important characterization of electromagnetic and weak transitions in atomic nuclei are sum rules. We focus on the non-energy-weighted sum rule (NEWSR), or total strength, and the energyweighted sum rule (EWSR); the ratio of the EWSR to the NEWSR is the centroid or average energy of transition strengths from an nuclear initial state to all allowed final states. These sum rules can be expressed as expectation values of operators, in the case of the EWSR a double commutator. While most prior applications of the double-commutator have been to special cases, we derive general formulas for matrix elements of both operators in a shell model framework (occupation space), given the input matrix elements for the nuclear Hamiltonian and for the transition operator. With these new formulas, we easily evaluate centroids of transition strength functions, with no need to calculate daughter states. We apply this simple tool to a number of nuclides, and demonstrate the sum rules follow smooth secular behavior as a function of initial energy, as well as compare the electric dipole (E1) sum rule against the famous Thomas-Reiche-Kuhn version. We also find surprising systematic behaviors for ground state electric quadrupole (E2) centroids in the sd-shell.K,M (ab), so the first term in (A1) is a linear summation of terms in the form ofwhere φ aeK = (−1) ja+je+K , other φ ··· are similar. We take (A9) into the 1st term in (A1), and end up with the expression for g ab in (23). The second term in (A1) is a linear summation of terms [(AWith (A6) it's straight forward to deriveLinear summations of the 1st term in the brace of (A11) lead to W 1 (abcd; J) and W 2 (abcd; J) in (25-26), the 2nd term to W 3 (abcd; J) in (27), and the 3rd term to W 4 (abcd; J) and W 5 (abcd; J) in (28)(29). The symmetry between (25-26) and (28-29) originates from here. We take the 1st term in the brace of (A11) as an example, and explain restrictions caused by Pauli's principle mentioned before. Use (A6) again to derive

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Section: Introductionmentioning

confidence: 99%

Transition sum rules in the shell model

Lü

Johnson

2018

Phys. Rev. C

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“…The validity of the Brink-Axel hypothesis for the GT strength function is not obvious and its violation is confirmed by the shellmodel Monte-Carlo studies at finite temperature[13] and most recently by the shell-model calculations for sd-shell nuclei[14].…”

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confidence: 99%

Thermal quasiparticle random-phase approximation calculations of stellar electron capture rates with the Skyrme effective interaction

Dzhioev¹,

Vdovin²,

Stoyanov

2019

Phys. Rev. C

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A microscopic thermodynamically consistent approach is applied to compute electron capture (EC) rates and cross sections on nuclei in hot stellar environments. The cross section calculations are based on the Donnelly-Walecka multipole expansion method for treatment of semi-leptonic processes in nuclei. To take into account thermal effects, we express the electron capture cross section in terms of temperature-and momentum-dependent spectral functions for respective multipole chargechanging operators. The spectral functions are computed by employing the self-consistent thermal quasiparticle random-phase approximation (TQRPA) with the Skyrme effective interaction. Three different Skyrme parametrizations (SkM * , SGII and SLy4) are used to investigate thermal effects on EC for 56 Fe and 78 Ni. For 56 Fe, the impact of thermally unblocked Gamow-Teller GT+ transitions on EC is discussed and the results are compared with those from shell-model calculations. In particular, it is shown that for some temperature and density regimes the TQRPA rates exceed the shell-model rates due to violation of the Brink-Axel hypothesis within the TQRPA. For neutron-rich 78 Ni, the full momentum-dependence of multipole transition operators is considered and it is found that not only thermally unblocked allowed 1 + transitions but also thermally unblocked first-forbidden 1 − and 2 − transitions favor EC. PACS numbers: 26.50.+x, 23.40.-s 21.60.Jz, 24.10.Pa, charge, longitudinal, transverse electric, and transverse magnetic multipole operators: σ J CL (E, T ) = (1 + a cos Θ)S MJ MJ + (1 + a cos Θ − 2b sin 2 Θ)S LJ LJ + E q (1 + a cos Θ) + c 2Re{S MJ LJ } (8) and σ J T (E, T ) = (1−a cos Θ+b sin 2 Θ) S T mag J T mag J +S T el J T el J

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“…We use experimental data where available and supplement with results from shell model calculations performed using OXBASH [8]. We employ a modified Brink-Axel hypothesis for high energy states [9]. Figure 1 shows our computed spectrum for 32 P; we chose the mass fraction X A,Z , temperature, density, and electron fraction Y e to match Fig.…”

Section: Charged Currentmentioning

confidence: 99%

Neutrinos from Pre-Collapse Stars

Misch¹,

Fuller²

2017

Proceedings of the 14th International Symposium on Nuclei in the Cosmos (NIC2016)

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We show that in order to make realistic predictions of the nuclear neutrino spectra from pre-collapse stellar cores, one must properly account for nuclear structure effects; often, the dominant nuclear transitions involve excited states, sometimes in both parent and daughter nuclei. We show that the standard technique of producing a neutrino energy spectrum by using a single effective transition structured to fit published neutrino production rates and energy losses will not accurately capture important spectral features.

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Modification of the Brink-Axel hypothesis for high-temperature nuclear weak interactions

Cited by 40 publications

References 56 publications

Transition sum rules in the shell model

Transition sum rules in the shell model

Thermal quasiparticle random-phase approximation calculations of stellar electron capture rates with the Skyrme effective interaction

Neutrinos from Pre-Collapse Stars

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