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Register a new userApplication of random phase approximation to vibrational excitations of double-$Lambda$ hypernuclei
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Using the Hartree-Fock plus random-phase-approximation (HF+RPA), we study the impurity effect of $Lambda$ hyperon on the collective vibrational excitations of double-$Lambda$ hypernuclei. To this end, we employ a Skyrme-type $Lambda N$ and $LambdaLambda$ interactions for the HF calculations, and the residual interactions for RPA derived with the same interactions. We find that inclusion of two $Lambda$ hyperons in $^{16}$O shifts the energy of the collective states towards higher energies. In particular, the energy of the giant monopole resonance of $^{,,18}_{LambdaLambda}$O, as well as that of $^{210}_{LambdaLambda}$Pb, becomes larger. This implies that the effective incompressibility modulus increases due to the impurity effect of $Lambda$ particle, if the $beta$-stability condition is not imposed.
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We discuss low-lying collective excitations of $Lambda$ hypernuclei using the self-consistent mean-field approaches. We first discuss the deformation properties of $Lambda$ hypernuclei in the $sd$-shell region. Based on the relativistic mean-field (RMF) approach, we show that the oblate deformation for $^{28}$Si nucleus may disappear when a $Lambda$ particle is added to this nucleus. We then discuss the rotational excitations of $^{25}_{Lambda}$Mg nucleus using the three-dimensional potential energy surface in the deformation plane obtained with the Skyrme-Hartree-Fock method. The deformation of $^{25}_{Lambda}$Mg nucleus is predicted to be slightly reduced due to an addition of $Lambda$ particle. We demonstrate that this leads to a reduction of electromagnetic transition probability, $B(E2)$, in the ground state rotational band. We also present an application of random phase approximation (RPA) to hypernuclei, and show that a new dipole mode, which we call a soft dipole $Lambda$ mode, appears in hypernuclei, which can be interpreted as an oscillation of $Lambda$ particle against the core nucleus.
We calculate the $Lambda Lambda to YN$ transition rate of ${^{phantom{Lambda}6}_{Lambda Lambda}}$He by the hybrid picture, the $pi$ and $K$ exchanges plus the direct quark processes. It is found that the hyperon-induced decay is weaker than the nucleon-induced decay, but the former may reveal the short-range mechanism of the weak transition and also give a clear signal of the strong $Delta I=3/2$ transition. The $Lambda Lambda to Y N$ transition in double-$Lambda$ hypernucleus is complement to the $Lambda N to NN$ transition as it occurs only in the J=0 channel, while the J=1 transition is dominant in the $Lambda N to NN$ case.
The non--mesonic weak decay of double--$Lambda$ hypernuclei is studied within a microscopic diagrammatic approach. Besides the nucleon--induced mechanism, $Lambda Nto nN$, widely studied in single--$Lambda$ hypernuclei, additional hyperon--induced mechanisms, $Lambda Lambdato Lambda n$, $Lambda Lambdato Sigma^0 n$ and $Lambda Lambdato Sigma^-p$, are accessible in double--$Lambda$ hypernuclei and are investigated here. As in previous works on single--$Lambda$ hypernuclei, we adopt a nuclear matter formalism extended to finite nuclei via the local density approximation and a one--meson exchange weak transition potential (including the ground state pseudoscalar and vector octets mesons) supplemented by correlated and uncorrelated two--pion--exchange contributions. The weak decay rates are evaluated for hypernuclei in the region of the experimentally accessible light hypernuclei $^{10}_{LambdaLambda}$Be and $^{13}_{LambdaLambda}$B. Our predictions are compared with a few previous evaluations. The rate for the $Lambda Lambdato Lambda n$ decay is dominated by $K$--, $K^*$-- and $eta$--exchange and turns out to be about 2.5% of the free $Lambda$ decay rate, $Gamma_{Lambda}^{rm free}$, while the total rate for the $Lambda Lambdato Sigma^0 n$ and $Lambda Lambdato Sigma^- p$ decays, dominated by $pi$--exchange, amounts to about 0.25% of $Gamma_{Lambda}^{rm free}$. The experimental measurement of these decays would be essential for the beginning of a systematic study of the non--mesonic decay of strangeness $-2$ hypernuclei. This field of research could also shed light on the possible existence and nature of the $H$--dibaryon.
We present an extension of the random--phase approximation (RPA) where the RPA phonons are used as building blocks to construct the excited states. In our model, that we call double RPA (DRPA), we include up to two RPA phonons. This is an approximate and simplified way, with respect to the full second random--phase approximation (SRPA), to extend the RPA by including two particle--two hole configurations. Some limitations of the standard SRPA model, related to the violation of the stability condition, are not encountered in the DRPA. We also verify in this work that the energy--weighted sum rules are satisfied. The DRPA is applied to low--energy modes and giant resonances in the nucleus $^{16}$O. We show that the model (i) produces a global downwards shift of the energies with respect to the RPA spectra; (ii) provides a shift that is however strongly reduced compared to that generated by the standard SRPA. This model represents an alternative way of correcting for the SRPA anomalous energy shift, compared to a recently developed extension of the SRPA, where a subtraction procedure is applied. The DRPA provides results in good agreeement with the experimental energies, with the exception of those low--lying states that have a dominant two particle--two hole nature. For describing such states, higher--order calculations are needed.
Recent progress has been experienced in the field of hypernuclear weak decay, especially concerning the ratio of the neutron- to proton-induced Lambda non-mesonic decay rates, G_n/G_p. Theoretical analyses of nucleon coincidence data have been performed in a finite nucleus framework. They led to the extraction of G_n/G_p values in agreement with pure theoretical estimates, thus providing an evidence for the solution of a longstanding puzzle. Here we present an alternative approach to the problem, based on a nuclear matter formalism extended to finite nuclei via the local density approximation. The work is motivated by the exigence to make the determination of G_n/G_p from data less model dependent. One-meson-exchange potentials are used for describing both the one- and two-nucleon induced decays, Lambda N -> n N and Lambda N N -> n N N. For the latter, treated within a microscopic approach, the channels Lambda n n -> n n n and Lambda p p -> n p p are included in addition to the mode Lambda n p -> n n p already considered, in a phenomenological way, in previous studies. The propagation of the final nucleons in the residual nucleus is simulated by an intranuclear cascade code. We evaluate single and double coincidence nucleon spectra for the non-mesonic decay of C-12-Lambda. Through the comparison of our predictions with KEK coincidence data we determine G_n/G_p=0.43 pm 0.10 for this hypernucleus, confirming previous finite nucleus analyses.
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