Thermodynamic properties of spin-polarized 3He gas in the temperature range 1 mK–4 K from the quantum second virial coefficient

2017 ◽  
Vol 31 (28) ◽  
pp. 1750202 ◽  
Author(s):  
A. F. Al-Maaitah ◽  
A. S. Sandouqa ◽  
B. R. Joudeh ◽  
H. B. Ghassib
Keyword(s):  
Thermodynamic Properties ◽  
Low Temperatures ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Matrix Inversion ◽  
Low Energy ◽  
Repulsive Interaction ◽  
Energy Limit ◽  
Temperature Range ◽  
Spin Polarized

The quantum second virial coefficient B[Formula: see text] of 3He[Formula: see text] gas is determined in the temperature range 0.001–4 K from the Beth–Uhlenbeck formula. The corresponding phase shifts are calculated from the Lippmann–Schwinger equation using a highly-accurate matrix-inversion technique. A positive B[Formula: see text] corresponds to an overall repulsive interaction; whereas a negative B[Formula: see text] represents an overall attractive interaction. It is found that in the low-energy limit, B[Formula: see text] tends to increase with increasing spin polarization. The compressibility Z is evaluated as another measure of nonideality of the system. Z becomes most significant at low temperatures and increases with polarization. From the pressure–temperature (P–T) behavior of 3He[Formula: see text] at low T, it is deduced that P decreases with increasing T below 8 mK.

The quantum second virial coefficient of 3He at low density in the temperature range 0.005–10 K

2017 ◽  
Vol 95 (12) ◽  
pp. 1208-1214 ◽  
Author(s):  
O.T. Al-Obeidat ◽  
A.S. Sandouqa ◽  
B.R. Joudeh ◽  
H.B. Ghassib ◽  
M.M. Hawamdeh
Keyword(s):  
First Principles ◽  
Virial Coefficient ◽  
Scattering Length ◽  
Second Virial Coefficient ◽  
Repulsive Interaction ◽  
Saturation Curve ◽  
Low Density ◽  
S Wave ◽  
Temperature Range ◽  
The Many

The quantum second virial coefficient Bq for 3He is calculated from first principles at low density in the temperature range 0.005–10 K. By “first principles”, it is meant that the many-body phase shifts are first determined within the Galitskii–Migdal–Feynman formalism; they are then plugged into the Beth–Uhlenbeck formula for Bq. A positive Bq corresponds to an overall repulsive interaction; a negative Bq represents an overall attractive interaction. The s-wave scattering length a0 is calculated quite accurately as a function of the temperature T. The effect of the (low-density) medium on Bq is studied. Bq is then used to determine the volume of 3He at the saturation curve. The compressibility is evaluated as a measure of the non-ideality of the system.

COMPRESSIBILITY OF GASES AT HIGH TEMPERATURES: I. METHODS OF MEASUREMENT AND APPARATUS

1949 ◽  
Vol 27b (4) ◽  
pp. 339-352 ◽  
Author(s):  
W. G. Schneider
Keyword(s):  
High Temperatures ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Temperature Range ◽  
Pure Helium ◽  
Methods Of Measurement

Methods and apparatus used for compressibility measurements of gases in the temperature range 0° to 600 °C. are described. A further method which can be used at temperatures above 600 °C. is also described. Data for some measurements with pure helium at 0° and at 600 °C. are given, from which the values (in Amagat units), 0.527 × 10−3 per atm. ± 0.003 × 10−3 and 0.439 × 10−3 per atm. ± 0.005 × 10−3 were obtained for the second virial coefficient at 0° and 600 °C. respectively.

scholarly journals Second virial coefficient for the exponent--spline-Morse-spline-van der Waals potential and its application

2021 ◽  
Author(s):  
E. Somuncu ◽  
B.A. Mamedov
Keyword(s):  
Experimental Data ◽  
Thermal Properties ◽  
Thermodynamic Properties ◽  
Virial Coefficient ◽  
Van Der Waals ◽  
Second Virial Coefficient ◽  
Rare Gases ◽  
Analytical Expression ◽  
Numerical Approaches ◽  
Binomial Function

An analytical expression for the second virial coefficient based on an exponent-spline-Morse-spline-van der Waals (ESMSV) potential is presented here for use in defining the thermodynamic properties of rare gases. Our method is established based on a series expansion of the exponential function, Meijer function, gamma function, binomial function, and hypergeometric function. Numerical approaches have commonly been used for the evaluation of the second virial coefficient with the ESMSV potential in the literature. The general formula obtained here can be applied to estimate the thermal properties of rare gases. Our results for the second virial coefficient based on the ESMSV potential of He-He, He-Ne, He-Ar, and He-Xe rare gases are compared with numerical calculations and experimental data, and it is shown that our analytical expression can be successfully used for other gases.

Spin-exchange scattering cross sections for hydrogen atoms at low temperatures

1980 ◽  
Vol 58 (6) ◽  
pp. 881-885 ◽  
Author(s):  
A. J. Berlinsky ◽  
B. Shizgal
Keyword(s):  
Cross Sections ◽  
Low Temperatures ◽  
Atomic Hydrogen ◽  
Spin Exchange ◽  
Low Energy ◽  
Energy Limit ◽  
Hydrogen Atoms ◽  
Exchange Scattering ◽  
Scattering Cross Sections

Calculations are presented of the low energy (0 < E ≤ 10−2 eV) spin exchange and frequency shift cross sections for (H,H) scattering, and of their thermal averages for 0 < T < 10 K. In particular, the behaviour of the cross sections in this low energy limit and the role of resonances due to orbiting collisions is studied in detail. A comparison is made with recent nmr measurements on gaseous atomic hydrogen at liquid helium temperatures. The results of this work suggest further useful experiments at low temperatures.

The classical and quantum second virial coefficient of low-density 132Xe vapor in the temperature-range 0.1 mK–30 000 K

2019 ◽  
Vol 95 (1) ◽  
pp. 015401 ◽  
Author(s):  
O T Al-Obeidat ◽  
A S Sandouqa ◽  
B R Joudeh ◽  
M M Hawamdeh ◽  
H B Ghassib
Keyword(s):  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Low Density ◽  
Temperature Range

scholarly journals HIGH AND LOW TEMPERATURE BEHAVIOR OF A QUANTUM GROUP FERMION GAS

1996 ◽  
Vol 11 (29) ◽  
pp. 2325-2333 ◽  
Author(s):  
MARCELO R. UBRIACO
Keyword(s):  
High Temperature ◽  
Low Temperature ◽  
Quantum Group ◽  
Upper Bound ◽  
Low Temperatures ◽  
Virial Coefficient ◽  
Second Virial Coefficient ◽  
Temperature Behavior ◽  
Spatial Dimensions ◽  
Fermion Gas

We consider the simplest SU q(2) invariant fermionic Hamiltonian and calculate the low and high temperature behavior for the two distinct cases q>1 and q<1. For low temperatures we find that entropy values for the Fermi case are an upper bound for those corresponding to q≠1. At high temperatures we find that the sign of the second virial coefficient depends on q, and vanishes at q=1.96. An important consequence of this fact is that the parameter q connects the fermionic and bosonic regions, showing therefore that SU q(2) fermions exhibit fractional statistics in three spatial dimensions.

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