On a method to correct for particle number fluctuations

Bang, J.; Krumlinde, J.; Nilsson, Sven Gösta

doi:10.1016/0031-9163(65)91127-3

Cited by 27 publications

(3 citation statements)

References 2 publications

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“…where the first three terms are the BeS ground state energy, and the last 29,30 term approximately accounts for the fixed-particle-numher correction.…”

Section: Pairing Spring Constantmentioning

confidence: 99%

Microscopic study of the variable-moment-of-inertia model for rare-earth nuclei

Chin

Tsang

1975

Phys. Rev. C

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LBL-2347Based on the microscopic cr~king model, the moment-of-inertia parameter .. deviate from the I(I+l) rule as the spins increase. Recently, it was discovered that at very high angular momenta, the rotational energies of some nuclei may exhibit anomalous behavior, the so called back-bending.l,2,3 We shall not discuss the back-bending phenomenon in this paper, but shall limit our calculations only to those states with moderate high spins.There exist many two-parameter formulas which fit very well the energy levels up to spin :r. with the inclusion of both quadrupole (12) and hexadecapole ('4) deformation.Since it has been shown that most of the two-parameter formulas are related to each other,7,17,24 we shall calculate specifically the parameters associated with the VMI model and the B coefficient connected with the 1 2 (I+l)2 term.The following section will briefly review the formulations developed in (I), the detailed calculations and formulas are given in Sec. III, and the last two sections will give the results and discussions.. .' . The VMI model can be expressed as follows: where -·1 a > is the deformed single particle state with a denoting the appropriate quantum numbers, m a -iST the~gnetic :quantumnnuJnber. along the· symmetry axis, U a and Va are the probability amplitudes in the presence of pairing interaction and Ea is the quasi-particle energy.The Inglis and Belyaev cranking formula (6) is based on the independent quasi-particle approximation. However, a recent calculation by Meyer, Speth 27 and Vogeler showed that the two carrection terms arising from the particleparticle and particle-hole interactions nearly cancel each other. It has also been shown by Rich 28 that correction due to particle-number conservation is also small. Thus it seems that the use of the cranking formula ·(6) is rather t,Tell justified numerically.The second term of Eq. (5) represents the fourth order cranking correction which was first studied by Harris 6 and the fourth order cranking 6 constant C n can be expressed as It is obvious from Eq. (5) thatThus, the contribution of the fourth order cranking in Eq. (4) The value of the force constant C VM1 or the B coefficient indicates the degree to which the spectrum deviates from the 1(1+1) rule. Both Eqs. (4) and (9) show that the contributions from various degrees of freedom are all posi.tblel1Z-"add~d.• with plus sign for protons and minus sign for neutrons. They also put in a linear surface dependence of G, which may be important for l~rge deformation.The BCS equation is then solved by including (15Z)1/2 or (lSN)1/2 states above and below the proton or neutron Fermi level.6. thus obtained are given in Table I. The pairing gap parameters 6. ,_'aridThe energy of a quasiparticle can be expressed as (12) where e: k is the single-particle energy and A is the chemical potential.Following (I) we parametrize the probability amplitudes {Uk' V k } by introducing a pairing correlation parameter VIf V = ~ (the energy gap ~ is the equilibirium value of V at ground state), Eq. ...

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“…where the first three terms are the BeS ground state energy, and the last 29,30 term approximately accounts for the fixed-particle-numher correction.…”

Section: Pairing Spring Constantmentioning

confidence: 99%

Microscopic study of the variable-moment-of-inertia model for rare-earth nuclei

Chin

Tsang

1975

Phys. Rev. C

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“…where EA=, is the total energy calculated without pairing (Nilsson-Strutinsky model with the spherical A = 146parameters [SI) and Ep& is the pairing energy (monopole BCS with blocking and an approximate particle number projection [6]). The total spin is identified with the sum of the quasiparticle's spin components along the symmetry axis [7].…”

Section: Pairing and Quadrupole Deformationmentioning

confidence: 99%

Competition between Pairing and Quadrupole Deformation in the Yrast Sequence of^150,152Dy

Åberg

1985

Phys. Scr.

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The yrast spectra are investigated for the non-collective nuclei 150i152D Y using the Nilsson-Strutinsky + blocked BCS model. The separate effects from the pairing force and the quadrupole force (deformation changes) are studied. It is found that the pairing force is important in describing the yrast line up to I -30, while the quadrupole force is important for I,> 20. The calculated increase of the oblate deformation with increasing spin is expained as an antipairing effect when only valence nucleons are building the total spin and as a polarization effect when the core becomes excited.

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“…[10][11][12] A more straightforward technique, first validated by the studies of Kerman et al, 4 has been to project particleconserving wave functions from the original BCS func tion and to use the former for the evaluation of all observables. 13 ' 14 Finally, we may mention some rather more elaborate efforts to construct wave functions for ground and exicted states, 15 * 16 including a method for obtaining exact solutions.…”

Section: Introductionmentioning

confidence: 99%

Number-Conserving Approximation for the Theory of the Pairing Interaction in Nuclei

Dans

Klein

1966

Phys. Rev.

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735results of this experiment indicate the persistence of rather sharp resonances through the giant-resonance region.Recently, Izumo 34,35 has presented a theory of "partial equilibrium" for nuclear reactions in which a few (3-7) nucleons share excitation energy. The model is an attempt to explain the existence of "intermediate reso nances^ or clumps of oscillator strength ranging in width from 100 to 400 keV. It may be that the reso nances observed in this experiment below 14 MeV are examples of such intermediate resonances.One prediction of the Izumo theory is that the reso-The pairing interaction is studied by means of the equations of motion. An approximation is derived which adheres strictly to particle-number conservation, but is otherwise quite close to the formalism of the Bardeen-Cooper-Schrieffer (BCS) theory. It yields ground-state energies and single-particle properties considerably improved over those of the latter theory, as evidenced by calculations for (i) the model of Pawlikowski and Rybarska, (ii) the model of the Ni isotopes solved exactly by Kerman, Lawson, and Mac Farlane. Though it does not yet surpass in accuracy several alternative improvements of the BCS theory, it is capable of systematic further development, including the treatment of more realistic potentials.

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On a method to correct for particle number fluctuations

Cited by 27 publications

References 2 publications

Microscopic study of the variable-moment-of-inertia model for rare-earth nuclei

Microscopic study of the variable-moment-of-inertia model for rare-earth nuclei

Competition between Pairing and Quadrupole Deformation in the Yrast Sequence of^150,152Dy

Number-Conserving Approximation for the Theory of the Pairing Interaction in Nuclei

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On a method to correct for particle number fluctuations

Cited by 27 publications

References 2 publications

Microscopic study of the variable-moment-of-inertia model for rare-earth nuclei

Microscopic study of the variable-moment-of-inertia model for rare-earth nuclei

Competition between Pairing and Quadrupole Deformation in the Yrast Sequence of150,152Dy

Number-Conserving Approximation for the Theory of the Pairing Interaction in Nuclei

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Competition between Pairing and Quadrupole Deformation in the Yrast Sequence of^150,152Dy