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arXiv:0803.4433

Creation of neutron spinless pairs in a superfluid liquid $^4$He and a neutron gas mixture

V. N. Minasyan

Published Mar 31, 2008• 1 citation
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Abstract

First, the creation of a free neutron spinless pairs is predicted in a superfluid liquid $^4$He and a neutron gas mixture. For solving the given problem, it is presented an exact solution to the model of dilute Bose gas as an extension of the Bogoliubov model, at quantity of the condensate fraction varying in the state $0\leq\frac{N_0}{N}\leq 1$, which in turn might be useful for a description of the superfluid liquid $^4$He. Due to an application of presented new model of dilute Bose gas, we prove that an appearance of atoms in the condensate is a suppressor for the collective modes as well as a creator for single-particle excitations On other hand, it is shown that the terms of the interaction between the Bogoliubov excitations (Bogoliubov phonon-roton modes) and the density modes of the neutron meditate an attractive interaction via the neutron modes, which in turn leads to a bound state on a spinless neutron pair.

DOI
10.48550/arxiv.0803.4433

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Creation of neutron spinless pairs in a superfluid liquid 4^44He and a neutron gas mixture
First, the creation of a free neutron spinless pairs is predicted in a superfluid liquid 4^44He and a neutron gas mixture. For solving the given problem, it is presented an exact solution to the model of dilute Bose gas as an extension of the Bogoliubov model, at quantity of the condensate fraction varying in the state 0≤N0N≤10\leq\frac{N_0}{N}\leq 10≤NN0​​≤1, which in turn might be useful for a description of the superfluid liquid 4^44He. Due to an application of presented new model of dilute Bose gas, we prove that an appearance of atoms in the condensate is a suppressor for the collective modes as well as a creator for single-particle excitations On other hand, it is shown that the terms of the interaction between the Bogoliubov excitations (Bogoliubov phonon-roton modes) and the density modes of the neutron meditate an attractive interaction via the neutron modes, which in turn leads to a bound state on a spinless neutron pair.
First, a condition for the Bose-Einstein transition in the superfluid liquid helium is presented due to the creation of a free neutron spinless pairs in a liquid helium and a dilute neutron gas mixture. We proposed a new model of dilute Bose gas, where presence atoms in the condensate is a suppressor for the collective modes as well as a creator for single-particle excitations On other hand, it is shown that the terms, of the interaction between the excitations of the Bose gas and the density modes of the neutron, meditate an attractive interaction via the neutron modes, which in turn leads to a bound state on a spinless neutron pair. The lambda transition is defined by a condition for the Bose-Einstein transition, which transforms reflected neutron pair modes to single neutron modes.
The paradoxes and disparities in the contemporary microscopic theory of superfluid helium (He–II) are discussed along with possible ways of resolving them by taking pair correlations of He4 atoms into consideration. It is shown that most paradoxes are associated with the commonly accepted initial assumption concerning the dominating role of single-particle Bose condensate (SPBC) in the quantum microstructure of the superfluid component ρs. The existence of intensive SPBC leads to a strong hybridization of the elementary excitation branches and to a common dispersion law for all boson branches, which is identified with the quasiparticle spectrum E(p) observed experimentally from slow neutron scattering in liquid helium. However, the stability of this spectrum during a transition through the λ-point and the large value of the gap in the vicinity of the “rotonic” minimum contradict both the Landau theoretical criterion of superfluidity and the small value of experimentally measured critical velocity. At the same time, a strong interaction between particles in the Bose liquid He4 strongly suppresses the SPBC which amounts to less than 1% of all He4 atoms and hence cannot be the main constituent of the superfluid component, unlike the case of a weakly nonideal Bose gas. Moreover, for a quite strong attraction between particles in a certain region of the momentum space, bound pairs of bosons can be formed in the superfluid Bose liquid, and a coherent pair condensate (CPC) analogous to the Cooper pair condensate in superconductors may appear. Such a strong CPC may completely suppress the weak SPBC. In this case, the one-particle spectrum ε(p) of elementary excitations does not hybridize with the collective (two-particle) spectrum and does not appear in the structure of the dynamic form factor S(p,ε), i.e., does not coincide with the spectrum measured from neutron scattering. The dispersion of one-particle spectrum is defined by the momentum dependence of the pair order parameter Ψ̃(p) and may have a minimum or a point of inflection at p≠0. This peculiarity in the one-particle spectrum of a Bose liquid with CPC but without SPBC vanishes together with Ψ̃(p) at the temperature Tc=Tλ of the phase transition from the superfluid to the normal state (unlike the rotonic minimum in the collective spectrum), while the corresponding critical velocity vc=min[ε(p)/p] vanishes at the λ-point in accordance with the Landau criterion and the experimental data. The assumption that the strong “Cooper-like” CPC is responsible for the quantum structure of the superfluid component ρs is confirmed indirectly by the successful application of the Justrow approximation (based on strong pair correlations) for describing the properties of liquid He4 and quantum liquid mixtures He3–4He on one hand, and by an anomalously large effective mass of He3 impurity atoms in He4, which is approximately equal to total mass of He3 and He4 atoms, thus pointing to the existence of helium atoms in superfluid liquid He–II. The value of the superfluid velocity circulation quantum in the Onsager–Feynman vortices in a Bose liquid with CPC but without SPBC is discussed as well as the critical velocities of superfluid He4 in ultrathin films and channels in which the creation and motion of quantum vortices are ruled out, and the quasiparticle spectrum undergoes dimensional quantization.
The spectrum of noncondensate excitations in neutron scattering on bosons is obtained in the framework of the Bogoliubov models both for liquid 4He and a dilute gas. The problem is solved using a path-integral representation of the partition function of the system. We describe the influence of scattering of neutrons on a Bose condensate in a stationary (time-independent) picture in the Gibbs equilibrium ensemble. This influence is a stationary boson response, and it depends on the initial neutron momentum k, transfer momentum p, and the neutron-boson interaction λ, which is related to the scattering length. The contribution of the neutrons to the initial Bogoliubov spectrum is found to be important for “quasi-elastic” scattering on the noncondensate, while the contribution of deep inelastic scattering is small; no contribution from elastic scattering on the Bose condensate is found. In the case of liquid Helium, the response is unlikely to be observable for all values p. On the other hand, for a gas one may expect a visible effect, in particular for a small momentum transfer p and a small density of the Bose condensate ϱ.
A self-consistent model of the superfluid (SF) state of a Bose liquid with strong interaction between bosons is considered, in which at T=0, along with a weak single-particle Bose-Einstein condensate (BEC), there exists an intensive pair coherent condensate (PCC) of bosons, analogous to the Cooper pair condensate of fermions. Such a PCC emerges due to an effective attraction between bosons in some regions of momentum space, which results from an oscillating sign-changing momentum dependence of the Fourier component V(p) of the interaction potential. The collective many-body effects of renormalization ("screening") of the initial interaction, which are described by the bosonic polarization operator Π(p,ω), lead to a suppression of the repulsion [V(p)>0] and an enhancement of the effective attraction [V(p)<0] in the respective domains of nonzero momentum transfer. The ratio of the BEC density n_0 to the total particle density n of the Bose liquid is used as a small parameter of the model. A closed system of nonlinear integral equations for the normal and anomalous self-energy parts is obtained with account for the terms of first order in the BEC density. In the framework of the ``soft spheres'' model with the single fitting parameter--the value of the repulsion potential at r=0, a theoretical quasiparticle spectrum E(p) is obtained, which is in good accordance with the experimental spectrum E_{exp}(p) of elementary excitations in superfluid 4^44He.
One considers the superfluid (SF) state of a Bose liquid with a strong repulsion between bosons, in which at T=0, along with a weak single-particle Bose-Einstein condensate (BEC), there exists an intensive pair coherent condensate (PCC), analogous to the Cooper condensate in a Fermi liquid with an attraction between the fermions. Such a PCC emerges in a system of bosons due to an oscillating sign-changing momentum dependence of the Fourier component of the pair interaction potential, which is characteristic of a certain family of repulsion potentials. In such cases, the Fourier component is negative in some domain of nonzero momentum transfer, which corresponds to an effective attraction. The collective effects of renormalization (``screening'') of the initial interaction lead to a suppression of the repulsion and an enhancement of the effective attraction. It is the ratio of the BEC density to the full density of the liquid n0/n≪1n_0/n\ll 1n0​/n≪1 that is used as a small parameter---unlike in the Bogolyubov theory for a quasi-ideal Bose gas, in which the small parameter is the ratio of the number of supracondensate excitations to the number of particles in an intensive BEC, (n−n0)/n0≪1(n-n_0)/n_0\ll 1(n−n0​)/n0​≪1. A closed system of nonlinear integral equations for the normal and anomalous self-energy parts is obtained, in the framework of a renormalized perturbation theory built on combined hydrodynamic and field variables. In the framework of the hard-spheres model, a spectrum of quasiparticles is obtained, which is in good accordance with the experimental spectrum of elementary excitations in superfluid 4^44He. The question of applicability of the Landau criterion in the absence of quantum vortices is discussed.
We study a superfluid Bose system with single-particle and pair condensates on the basis of a half-phenomenological theory of a Bose liquid not involving the weakness of interparticle interaction.The coupled equations describing the equilibrium state of such system are derived from the variational principle for entropy.These equations are analyzed at zero temperature both analytically and numerically.It is shown that the fraction of particles in the single-particle and pair condensates essentially depends on the total density of the system.At densities attainable in condensates of alkali-metal atoms, almost all particles are in the single-particle condensate.The pair condensate fraction grows with an increasing total density and becomes dominant.It is shown that at density of liquid helium, the single-particle condensate fraction is less than 10%, which agrees with experimental data on inelastic neutron scattering, Monte Carlo calculations and other theoretical predictions.The ground state energy, pressure, and compressibility are found for the system under consideration.The spectrum of single-particle excitations is also analyzed.