Intrinsic asymmetry parameter in nonmesonic hypernuclear decay: analytical proof of the independence on hypernucleus within an independent particle shell model

C. BARBERO AND A. MARIANO

BRAZILIAN JOURNAL OF PHYSICS

SOC BRASILEIRA FISICA

Año: 2009 vol. 39 p. 91 - 97

0103-9733

We derive general analytical expressions for the evaluation of theintrinsic asymmetry parameter in nonmesonic hypernuclear weakdecay, within an independent particle shell model framework.Present formalism is valid for even-even, even-odd and odd-oddcore hypernucleus. A standard strangeness-changing weak transitionpotential with exchange of the complete meson octet($pi,eta,K, ho,omega,K^*$) is assumed.  Very simple analyticalformulas are obtained within the $s$-wave approximation when werestrict to the $pi$ and $pi+K$ exchange models, providing anuseful and manageable tool to understand the origin of thediscrepancies between theoretical and experimental results.Numerical values for $^{4}_Lambda He$, $^{5}_Lambda He$,$^{11}_Lambda B$, $^{12}_Lambda C$, $^{16}_Lambda O$,$^{17}_Lambda O$ and $^{28}_Lambda Si$ hypernuclei areexhibited. Present formalism could be used to understand why newcontributions to the exchange potential allow to obtain goodagreement with data, as indicated in very recent works. Thenecessity of a consistent inclusion of: i) different modificationsof the exchange potential (two-pion exchange, $a_1$ meson, $DeltaT=3/2$ terms coming from vector mesons, etc); ii) final stateinteractions on primary nucleons inside the residual nucleus andalso correlations between the free emitted ones; and iii)configuration mixing in the final system, is remarked.