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[en] In traditional thermodynamics it is assumed that isentropic, reversible, adiabatic processes can be summoned up on demand and straightforwardly accomplished. By contrast, taking entropy as the maximised uncertainty of a final equilibrium state of a quantised system, it is not obvious that an associated process can always be found that is both rigorously isentropic and reversibly adiabatic. In fact, we find that linear relations between generalized forces Xj (such as pressures Pj) and energies Ej are necessary and sufficient conditions for a reversible quasi-static and adiabatic change to be truly isentropic. However, such relationships only hold for a few especially simple systems, such as the perfect gas and the idealised paramagnet. They do not generally hold to all orders for more complicated systems. By considering the associated entropy increases up to second order in small changes of the conjugate displacements (such as the volume Vj) we argue that the consequences are nevertheless in practice negligible. (paper: quantum statistical physics, condensed matter, integrable systems)
[en] The excitation energies of states belonging to the ground state bands of heavy even–even nuclei are analysed using recurrence relations. Excellent agreement with experimental data at the 10 keV level is obtained by taking into account strong correlations which emerge in the analysis. This implies that the excitation energies can be written as a polynomial of maximum degree 4 in the angular momentum. (paper)
[en] We generate the core-cluster partitions of even-even nuclei in the rare-earth region using a form of the core-cluster interaction employed previously in an analysis of nuclei in the actinide region. The correlations between the core-cluster charge products thus obtained and various nuclear observables are found to display similar characteristics in the two mass regions
[en] We first give a brief review of our earlier empirical work on parameter-free difference equations for nuclear spectra and discuss some of the implications. Then we show that a simple quantum mechanical model is capable of explaining and improving our previously suggested recursion relations.
[en] It is known that coupling an intrinsic excitation of integer spin and positive parity I+ to a rotor having a degenerate set of states Lπ=0+,2+,4+,..., generates a series of K bands. A given value of I+ gives rise to several bands labeled by K+=0+,1+,2+,...,I+, that is, a total of (I+1) such bands, in the spectrum of the combined system. We discuss how a binary cluster model of an excited core orbited by a spinless cluster can approximate these conditions. A crucial point is that the radial wave functions of relative motion are very similar for low L, and their radial coupling integrals even more so, such that the wave functions play the model role of a common intrinsic state for the lowest excited states of the system. If the core has a 0+ ground state and a low-lying 2+ excited state, then lifting the degeneracy leads to a ground state K+=0+ band and low-lying excited K+=0+, 1+, and 2+ bands. Although these are all seen in light nuclei, the K+=1+ band is conspicuous by its apparent absence in heavy nuclei, and we urge experimental groups to reexamine their data for signs of it.
[en] We show that the ground-state band spectra of very many rare-earth and actinide nuclei appear to obey simple recurrence relations. Our initial empirical observation is then refined to suggest a new method for predicting higher lying members of a band from lower lying known members
[en] We describe the low-lying negative parity states of 238U in terms of a Pb-Ne cluster model. The Pb core is in an excited 3- state and the relative orbital motion has angular momentum values L = 0, 2, 4, .... The two bodies interact through central and second rank tensor potentials, leading to four bands loosely labelled by the rotational model notation of Kπ = 0-, 1-, 2-, 3-. However, the coupling between core and cluster is of intermediate strength, leading to an irregular pattern of energy differences, in particular inverted doublets in the Kπ = 1- band. Remarkably, the main features of the predicted spectrum are borne out by experiment
[en] In a binary cluster model the likely core-cluster decompositions of a nucleus involve especially stable cores and/or clusters. This criterion often gives rise to a number of preferred decompositions, each with different physical attributes. These differences are particularly acute for 212Po, and we examine the properties of the bands generated by the core-cluster decompositions of this nucleus into (208Pb+4He) and (132Te+80Ge)
[en] Many heavy nuclei have low-lying Kπ = 0- bands. Furthermore, several even isotopes of Ra, Th, U and Pu have Kπ = 1- bands with bandhead excitation energies very close to 1 MeV. The E3 transitions from the 0+ ground state to the 3- members of these bands have reduced strengths B(E3; 0+ → 3-) comparable to those measured in the isotopes of Pb. An exotic cluster model with a Pb core is proposed to account for these observations. A good account of the data is given, and higher lying Kπ = 2- and 3- bands are predicted. The intermediate strength quadrupole-quadrupole coupling between cluster and core leads to irregular, inverted doublets in the calculated Kπ = 1- bands