Mass-ratio parameters expressions for binary clasters of identical fermion systems

R.K. Kalinauskas, Darius Germanas, Saulius Mickevičius

Published Jan 1, 2012• 0 citations

Abstract

In this contribution, we present the explicit expressions of mass-ratio parameters for binary clasters composed of n(1), and n(2) particles which can be used developing efficient techniques for large-scale calculations of the coefficients of fractional parentage (CFP) for systems consisting of n = n(1) + n(2) identical fermions.

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Abstract

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P_{N_1 ,N}

in a subspace where N 1 and N 2 = N − N 1 nucleons basis states are already antisymmetrized. The main result of this paper is that according to permutation operators

P_{N_1 ,N}

eigenvalues we can distinguish totally asymmetrical N particle states from the other states with lower degree of asymmetry.

We study the dimer-dimer scattering length

{a}_{4}

for a two-component Fermi mixture in which the different fermions have different masses ${m}_{\ensuremath{\uparrow}}$ and ${m}_{\ensuremath{\downarrow}}$. This is made in the framework of the exact field-theoretic method. In the large mass ratio domain the equations are simplified enough to lead to an analytical solution. In particular we link

{a}_{4}

to the fermion-dimer scattering length

{a}_{3}

for the same fermions and obtain the very simple relation

{a}_{4}={a}_{3}/2

. The result ${a}_{4}\ensuremath{\simeq}{a}_{3}/2$ is actually valid whatever the mass ratio with quite good precision. As a result we find an analytical expression providing

{a}_{4}

with fairly good precision for any mass. To dominant orders for large mass ratio it agrees with the literature. We show that in this large mass ratio domain, the dominant processes are the repeated dimer-dimer Born scatterings, considered earlier by Pieri and Strinati [Phys Rev. B 61, 15370 (2000)]. We conclude that their approximation of retaining only these processes is a fairly good one whatever the mass ratio.