Abstract. The astrophysical S-factor of p 2 H radiative capture in the energy range down to 1 keV is considered in the potential cluster model with the classification of orbital states according to Young's scheme symmetry. It is shown that the approach used, which takes into account the E1 transition only, gives a good description of the new experimental data for two potentials of the bound state of the The radiative p + 2 H → 3 He + γ capture is a part of the hydrogen cycle and gives a considerable contribution to the energy efficiency of thermonuclear reactions [1] which account for burning of the Sun and stars of our Universe. The interacting nuclear particles of the hydrogen cycle have a minimal value which is a potential barrier. Thus, it is the first chain of nuclear reactions which can take place at ultralow energies and star temperatures. Then, for this chain, the process of the radiative p 2 H capture is the basic process for the transition from the primary proton fusion p + p → 2 H + e − + ν e to the final process 3 He+ 3 He → 4 He+2p [2] in the p-p chain. That is why the theoretical and experimental investigation of the radiative p 2 H capture in detail is of fundamental interest not only for nuclear astrophysics, but also for nuclear physics of ultralow energies and lightest atomic nuclei.We will discuss the astrophysical S-factors on the basis of a potential cluster model which takes into account the supermultiplet symmetry of wave functions (WF) with the splitting of orbital states according to Young's schemes. This approach allows us to analyse the structure of inter-cluster interactions, detecting allowed and forbidden states in the interaction potential, and thus, the number of WF nodes of the relative motion of clusters [3,4].The total cross-sections of the photoprocesses of the lightest nuclei were considered in this approach in our work [4]. E1 transitions resulting from the orbital part of the electric operator Q Jm (L) were taken into account in these calculations of the photodecays of 3 He and 3 H a e-mail: albert-j@yandex.ru nuclei into p 2 H and n 2 H channels. The values of E2 crosssections and cross-sections depending on the spin part of the electric operator turned out to be several times less. Further, it was assumed that E1 electric transitions in the N 2 H system are possible between the "pure" (scheme {3}) 2 S state of 3 H and 3 He nuclei and the doublet 2 P scattering state mixed according to Young's schemes {3} + {21}.To calculate photonuclear processes in the systems under consideration the nuclear part of the potential of intercluster p 2 H and n 2 H interactions is represented aswith a point-like Coulomb potential, V 0 -the Gaussian attractive part, and V 1 -the exponential repulsive part. The potential of each partial wave was constructed so that it would correctly describe the respective partial phase shift of the elastic scattering [5]. Using this concept, the potentials of the p 2 H interaction for scattering processes were received, parameters of such potentials were ful...

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It is well-known that the Liouville equation of statistical mechanics is restricted to systems where the total number of particles (N) is fixed. In this paper, we show how the Liouville equation can be extended to systems where the number of particles can vary, such as in open systems or in systems where particles can be annihilated or created. A general conservation equation for an arbitrary dynamical variable is derived from the extended Liouville equation following Irving and Kirkwood's 2 technique. From the general conservation equation, the particle number conservation equation is obtained that includes general terms for the annihilation or creation of particles. It is also shown that the grand canonical ensemble distribution function is a particular stationary solution of the extended Liouville equation, as required. In general, the extended Liouville equation can be used to study nonequilibrium systems where the total number of particles can vary.

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The manuscript is devoted to the description of the results obtained in the frame of the modified potential cluster model with the classification of states according to Young tableaux for neutron and proton radiative capture processes on 2 H at thermal and astrophysical energies. It demonstrates methods of application that were obtained on the basis of phase shift analysis and characteristics of the bound states of 2 H potentials for consideration of the radiative capture processes. First reaction of the proton capture directly takes part in the pp solar cycle, where it is the second reaction. The neutron capture is not a part of usual thermonuclear cycles in the Sun and stars, but can take part in the processes of primordial nucleosynthesis, following at formation and evolution of our entire Universe.

Astrophysical S-factors of radiative capture reactions on light nuclei have been calculated in a two-cluster potential model, taking into account the separation of orbital states by the use of Young schemes. The local two-body potentials describing the interaction of the clusters were determined by fitting scattering data and properties of bound states. The many-body character of the problem is approximatively accounted for by Pauli forbidden states. An important feature of the approach is the consideration of the dependence of the interaction potential between the clusters on the orbital Young schemes, which determine the permutation symmetry of the nucleon system. Proton capture on 2 H, 6 Li, 7 Li, 12 C, and 13 C was analyzed in this approach. Experimental data at low energies were described reasonably well when the phase shifts for cluster-cluster scattering, extracted from precise data, were used. This shows that decreasing the experimental error on differential elastic scattering cross sections of light nuclei at astrophysical energies is very important also to allow a more accurate phase shift analysis. A future increase in precision will allow more definite conclusions regarding the reaction mechanisms and astrophysical conditions of thermonuclear reactions.

The total cross-sections of the radiative neutron capture processes on 9 Be, 14 C, 14 N, 15 N and 16 O are described in the framework of the modified potential cluster model with the classification of orbital states according to Young tableaux. The continued interest in the study of these reactions is due, on the one hand, to the important role played by this process in the analysis of many fundamental properties of nuclei and nuclear reactions, and, on the other hand, to the wide use of the capture cross-section data in the various applications of nuclear physics and nuclear astrophysics, and, also, to the importance of the analysis of primordial nucleosynthesis in the Universe. This article is devoted to the description of results for the processes of the radiative neutron capture on certain light atomic nuclei at thermal and astrophysical energies. The considered capture reactions are not part of stellar thermonuclear cycles, but involve in the reaction chains of inhomogeneous Big Bang models.Keywords: Nuclear astrophysics; primordial nucleosynthesis; light atomic nuclei; low and astrophysical energies; phase shift analysis of the n 16 O scattering; radiative capture; total cross-section; thermonuclear processes; potential cluster model; forbidden states. PACSNumber(s): 21.60.Gx, 25.20.Lj, 25.40.Lw, 26.20.Np, 26.35.+c, 26.50.+x, 26.90.+n, 98.80.Ft 1350075-1 Int. J. Mod. Phys. E 2013.22. Downloaded from www.worldscientific.com by STOCKHOLM UNIVERSITY on 08/14/15. For personal use only. 1350075-2 Int. J. Mod. Phys. E 2013.22. Downloaded from www.worldscientific.com by STOCKHOLM UNIVERSITY on 08/14/15. For personal use only. 1350075-4 Int. J. Mod. Phys. E 2013.22. Downloaded from www.worldscientific.com by STOCKHOLM UNIVERSITY on 08/14/15. For personal use only. Radiative Neutron Capture on 9 Be, 14 C, 14 N , 15 N and 16 O Model and Calculation MethodsThe expressions for the total radiative capture cross-sections σ(NJ , J f ) in the PCM are given, for example, in Refs. 29 and 30 are written aswhere for the electric orbital EJ(L) transitions (S i = S f = S) we have 29 :

The possibility of describing available experimental data for the total cross sections of neutron radiative capture on 8Li at thermal and astrophysical energies was considered within the framework of the modified potential cluster model with the state classification of nuclear particles according to the Young tableaux. Our approach allows one to transmit available data in the energy range 0.1–1.0 MeV quite well, and predicts the behavior of the total cross sections at super-low energies, down to 25.3 × 10−9 MeV.