Structure of LargeH3e−H4

Abstract

We have investigated how helium atoms are distributed within a mixed 3 He N3 -4 He N4 large drop with N 3 ¿ N 4 . For drops doped with a SF 6 molecule or a Xe atom, we have found that the number of 3 He atoms within the volume containing the first two solvation shells increases when N 4 decreases in such a way that these dopants may be in a superfluid environment for N 4 $ 60, which gradually disappears as N 4 decreases. The result is in qualitative agreement with recent experimental data.[ S0031-9007(99) [7] Monte Carlo calculations. It is remarkable that the presence of the impurity, which causes the 4 He density to rise up to several times the saturation value, is not destroying its superfluid character, and that, in spite of the high densities reached, the first solvation shell remains liquid [8]. An indication of this fluidlike behavior is that the peak density in the first solvation shell continues to increase as the second shell grows [9].Even if the intrepretation of the microscopic Andronikashvili experiment is on a firm basis, a remaining major question is how 3 He is distributed around the 4 Heplus-impurity complex, and, in general, how liquid 3 He is dissolved into 4 He droplets at very low temperatures. These are the questions we want to address in this paper.At zero temperature, it is known that the maximum solubility of 3 He in the bulk of 4 He is ϳ6.6% [10]. For liquid 4 He systems having a free surface, it is also known that a large amount of 3 He is accumulated on the free surface occupying Andreev states [11,12] before it starts being dissolved into the bulk. In the case of drops made of up to several thousand atoms, the surface region constitutes a sizeable part of the system [13], and the surface has a large capacity for storing 3 He atoms before they get inside the drop [14]. Because of the wide free surface of both isotopes [15,16] and the low surface tension of the 3 He-4 He liquid interface [17], one expects that this region plays a prominent role when it constitutes a large part of the system or, as in the present case, when it is close to the dopant atom or molecule.The structure and energetics of mixed, doped or not, helium droplets have been addressed using a finite-range density functional method [14]. That work was carried out before the experiments reported in Ref. [1], and the emphasis was put on improving the density functional method to better describe the thermodynamical properties of the liquid mixture, and to study rather small mixed droplets with N 4 ¿ N 3 . Our main goal here is to apply the density functional method to droplets whose characteristics are closer to those of the experiments, with the restriction of spherical symmetry for the He-impurity potential for the sake of simplicity. We have considered Xe and SF 6 as dopants, using for the latter a spherically averaged interaction potential. The Xe-He potential is weaker than the SF 6 -He potential. In this respect, our results for that atomic impurity should better represent the experimental ones for OCS even if thi...

Experimental and theoretical study of the radial density distributions of large3Hedroplets

“…The 3 He gas used is 99.9% pure with the remaining 0.1% impurity being mostly 4 He. This small amount of 4 He is concentrated at the center of the droplet 35 and cannot affect the surface properties of the system. The droplet velocity distributions were measured and found to be reasonably narrow (⌬ / р2%) with mean speeds of between 250 and 400 m/s.…”

“…As in Ref. 35 the large number of 3 He atoms in the droplets justifies the use of the extended Thomas-Fermi method to express the kinetic energy density as a function of the particle density and its gradients. 18 For a given 3 He N droplet, the Euler-Langrange equation…”

Quantized Vortices in MixedH3e−H4Mayol1, Pí2, Barranco3 et al. 2001Phys. Rev. Lett.Self Cite221110View full textAdd to dashboardCite

“…We checked that these changes have negligible effects on the relevant results, while they drastically reduce the numerical effort. As discussed in [9,10], the density functional contains a set of parameters which is fixed to reproduce static properties of pure and mixed He systems at zero temperature, such as the equation of state, surface tension of the different interfaces, the osmotic pressure, and maximum solubility of 3 He into 4 He [13].As in [5], the vortex line is included through the Feynman-Onsager ansatz, i.e., by adding an extra centrifugal energy associated with the velocity field of 4 He, which is singular on the vortex axis, thus forcing its density to vanish. For doped droplets, one has to include the heliumimpurity interaction, which acts as an external potential in 145301-1 0031-9007͞01͞ 87(14)͞145301(4)$15.00…”

“…Our starting point is a density functional previously developed for mixed 3 He-4 He systems, which allows one to write the energy of the mixture as E R dr H ͓r 3 ͑r͒, r 4 ͑r͔͒, where r 3 ͑r͒ [r 4 ͑r͔͒ is the 3 He [ 4 He] particle density (see [9,10], and references therein). To keep the already cumbersome calculations at an affordable level, here we use a slightly simplified version of the same functional; namely, we take the core of the screened Lennard-Jones He-He potentials as in the original OrsayParis functional [11], and drop the gradient-gradient term which appears in the Orsay-Trento functional [12] for 4 He.…”

“…We checked that these changes have negligible effects on the relevant results, while they drastically reduce the numerical effort. As discussed in [9,10], the density functional contains a set of parameters which is fixed to reproduce static properties of pure and mixed He systems at zero temperature, such as the equation of state, surface tension of the different interfaces, the osmotic pressure, and maximum solubility of 3 He into 4 He [13].…”