The Lipkin Model in the su(M+1)-Algebra for Many-Fermion System and its Counterpart in the Schwinger Boson Representation

Following the Schwinger boson representation for the su(M+1)- and the su(N,1)-algebra presented by two of the present authors (J. da P. and M. Y.) and Kuriyama, a possible counterpart of the Lipkin model in the su(M+1)-algebra formulated in the fermion space is presented. The free vacuum, which plays a fundamental role in the conventional treatment of the Lipkin model, is generalized in a quite natural way, and further, the excited state generating operators such as the particle-hole pairs are also given in a natural scheme. As concrete examples, the cases of the su(2)-, su(3)- and the su(4)-algebra are discussed. Especially, the case of the su(4)-algebra is investigated in detail in relation to the nucleon pairing correlations and the high temperature superconductivity.Comment: 22 pages, 1 figure, using PTPTeX styl

The Interference Term between the Spin and Orbital Contributions to M1 Transitions

We study the cross-correlation between the spin and orbital parts of magnetic dipole transitions M1 in both isoscalar and isovector channels. In particular, we closely examine certain cases where $\sum B(M1)$ is very close to $\sum B(M1)_{\sigma} + \sum B(M1)_l$, implying a cancellation of the summed interference terms. We gain some insight into this problem by considering special cases approaching the SU(3) limit, and by examining the behaviour of single-particle transitions at the beginning and towards the end of the s-d shell.Comment: 9 pages of latex file and no figure

Systematic study of proton-neutron pairing correlations in the nuclear shell model

A shell-model study of proton-neutron pairing in $2p1f$ shell nuclei using a parametrized hamiltonian that includes deformation and spin-orbit effects as well as isoscalar and isovector pairing is reported. By working in a shell-model framework we are able to assess the role of the various modes of proton-neutron pairing in the presence of nuclear deformation without violating symmetries. Results are presented for $^{44}$Ti, $^{45}$Ti, $^{46}$Ti, $^{46}$V and $^{48}$Cr to assess how proton-neutron pair correlations emerge under different scenarios. We also study how the presence of a one-body spin-obit interaction affects the contribution of the various pairing modes.Comment: 12 pages, 16 figure

Classification of states of single-jj fermions with JJ-pairing interaction

In this paper we show that a system of three fermions is exactly solvable for the case of a single-$j$ in the presence of an angular momentum-$J$ pairing interaction. On the basis of the solutions for this system, we obtain new sum rules for six-$j$ symbols. It is also found that the "non-integer" eigenvalues of three fermions with angular momentum $I$ around the maximum appear as "non-integer" eigenvalues of four fermions when $I$ is around (or larger than) $J_{\rm max}$ and the Hamiltonian contains only an interaction between pairs of fermions coupled to spin $J=J_{\rm max}=2j-1$. This pattern is also found in five and six fermion systems. A boson system with spin $l$ exhibits a similar pattern.Comment: to be published in Physical Review

Patterns of the ground states in the presence of random interactions: nucleon systems

We present our results on properties of ground states for nucleonic systems in the presence of random two-body interactions. In particular we present probability distributions for parity, seniority, spectroscopic (i.e., in the laboratory framework) quadrupole moments and $\alpha$ clustering in the ground states. We find that the probability distribution for the parity of the ground states obtained by a two-body random ensemble simulates that of realistic nuclei: positive parity is dominant in the ground states of even-even nuclei while for odd-odd nuclei and odd-mass nuclei we obtain with almost equal probability ground states with positive and negative parity. In addition we find that for the ground states, assuming pure random interactions, low seniority is not favored, no dominance of positive values of spectroscopic quadrupole deformation, and no sign of $\alpha$-cluster correlations, all in sharp contrast to realistic nuclei. Considering a mixture of a random and a realistic interaction, we observe a second order phase transition for the $\alpha$-cluster correlation probability.Comment: 7 page

Monopole Excitation to Cluster States

We discuss strength of monopole excitation of the ground state to cluster states in light nuclei. We clarify that the monopole excitation to cluster states is in general strong as to be comparable with the single particle strength and shares an appreciable portion of the sum rule value in spite of large difference of the structure between the cluster state and the shell-model-like ground state. We argue that the essential reasons of the large strength are twofold. One is the fact that the clustering degree of freedom is possessed even by simple shell model wave functions. The detailed feature of this fact is described by the so-called Bayman-Bohr theorem which tells us that SU(3) shell model wave function is equivalent to cluster model wave function. The other is the ground state correlation induced by the activation of the cluster degrees of freedom described by the Bayman-Bohr theorem. We demonstrate, by deriving analytical expressions of monopole matrix elements, that the order of magnitude of the monopole strength is governed by the first reason, while the second reason plays a sufficient role in reproducing the data up to the factor of magnitude of the monopole strength. Our explanation is made by analysing three examples which are the monopole excitations to the $0^+_2$ and $0^+_3$ states in $^{16}$O and the one to the $0^+_2$ state in $^{12}$C. The present results imply that the measurement of strong monopole transitions or excitations is in general very useful for the study of cluster states.Comment: 11 pages, 1 figure: revised versio

The effect of short-term intermittent hypoxic exposure on heart rate variability in a sedentary population

While the effects of instantaneous, single-bout exposure to hypoxia have been well researched, little is known about the autonomic response during, or as an adaptation to, repeated intermittent hypoxic exposure (IHE) in a sedentary population. Resting heart rate variability (HRV) and exercise capacity was assessed in 16 participants (8 receiving IHE, [Hyp] and 8 receiving a placebo treatment [C]) before and after a 4-week IHE intervention. Heart rate variability was also measured during an IHE session in the last week of the intervention. Post-intervention, the root mean squared successive difference (rMSSD) increased substantially in Hyp (71.6 ± 52.5%, mean change ± 90% confidence limits) compared to C suggesting an increase in vagal outflow. However, aside from a likely decrease in submaximal exercise heart rate in the Hyp group (–5.0 ± 6.4%) there was little evidence of improved exercise capacity. During the week 4 IHE measurement, HRV decreased during the hypoxic exposure (reduced R-R interval: –7.5 ± 3.2%; and rMSSD: –24.7 ± 17.3%) suggesting a decrease in the relative contribution of vagal activity. In summary, while 4 weeks of IHE is unlikely to improve maximal exercise capacity, it may be a useful means of increasing HRV in people unable to exercise