Superfluidity of a condensate with np pairing correlations in asymmetric nuclear matter

Influence of asymmetry on superfluidity of nuclear matter with triplet-singlet pairing of nucleons (in spin and isospin spaces) is considered within the framework of a Fermi-liquid theory. Solutions of self-consistent equations for the energy gap at T=0 are obtained. It is shown, that if the chemica...

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Дата:	2001
Автори:	Akhiezer, A.I., Isayev, A.A., Peletminsky, S.V., Yatsenko, A.A.
Формат:	Стаття
Мова:	English
Опубліковано:	Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2001
Назва видання:	Вопросы атомной науки и техники
Теми:	Quantum fluids
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Цитувати:	Superfluidity of a condensate with np pairing correlations in asymmetric nuclear matter / A.I. Akhiezer, A.A. Isayev, S.V. Peletminsky, A.A. Yatsenko // Вопросы атомной науки и техники. — 2001. — № 6. — С. 334-338. — Бібліогр.: 13 назв. — англ.

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spelling	irk-123456789-800452015-04-10T03:03:01Z Superfluidity of a condensate with np pairing correlations in asymmetric nuclear matter Akhiezer, A.I. Isayev, A.A. Peletminsky, S.V. Yatsenko, A.A. Quantum fluids Influence of asymmetry on superfluidity of nuclear matter with triplet-singlet pairing of nucleons (in spin and isospin spaces) is considered within the framework of a Fermi-liquid theory. Solutions of self-consistent equations for the energy gap at T=0 are obtained. It is shown, that if the chemical potentials of protons and neutrons are determined in the zero gap width approximation, then the energy gap for some values of density and asymmetry parameter of nuclear matter demonstrates double-valued behavior. However, with account for the feedback of pairing correlations through the normal distribution functions of nucleons two-valued behavior of the energy gap turns into universal one-valued behavior. At T=0 the energy gap has a discontinuities as a function of density in a narrow layer model. These discontinuities depend on the asymmetry parameter. 2001 Article Superfluidity of a condensate with np pairing correlations in asymmetric nuclear matter / A.I. Akhiezer, A.A. Isayev, S.V. Peletminsky, A.A. Yatsenko // Вопросы атомной науки и техники. — 2001. — № 6. — С. 334-338. — Бібліогр.: 13 назв. — англ. 1562-6016 PACS: 21.65.+f; 21.30.Fe; 71.10.Ay http://dspace.nbuv.gov.ua/handle/123456789/80045 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Quantum fluids Quantum fluids
spellingShingle	Quantum fluids Quantum fluids Akhiezer, A.I. Isayev, A.A. Peletminsky, S.V. Yatsenko, A.A. Superfluidity of a condensate with np pairing correlations in asymmetric nuclear matter Вопросы атомной науки и техники
description	Influence of asymmetry on superfluidity of nuclear matter with triplet-singlet pairing of nucleons (in spin and isospin spaces) is considered within the framework of a Fermi-liquid theory. Solutions of self-consistent equations for the energy gap at T=0 are obtained. It is shown, that if the chemical potentials of protons and neutrons are determined in the zero gap width approximation, then the energy gap for some values of density and asymmetry parameter of nuclear matter demonstrates double-valued behavior. However, with account for the feedback of pairing correlations through the normal distribution functions of nucleons two-valued behavior of the energy gap turns into universal one-valued behavior. At T=0 the energy gap has a discontinuities as a function of density in a narrow layer model. These discontinuities depend on the asymmetry parameter.
format	Article
author	Akhiezer, A.I. Isayev, A.A. Peletminsky, S.V. Yatsenko, A.A.
author_facet	Akhiezer, A.I. Isayev, A.A. Peletminsky, S.V. Yatsenko, A.A.
author_sort	Akhiezer, A.I.
title	Superfluidity of a condensate with np pairing correlations in asymmetric nuclear matter
title_short	Superfluidity of a condensate with np pairing correlations in asymmetric nuclear matter
title_full	Superfluidity of a condensate with np pairing correlations in asymmetric nuclear matter
title_fullStr	Superfluidity of a condensate with np pairing correlations in asymmetric nuclear matter
title_full_unstemmed	Superfluidity of a condensate with np pairing correlations in asymmetric nuclear matter
title_sort	superfluidity of a condensate with np pairing correlations in asymmetric nuclear matter
publisher	Національний науковий центр «Харківський фізико-технічний інститут» НАН України
publishDate	2001
topic_facet	Quantum fluids
url	http://dspace.nbuv.gov.ua/handle/123456789/80045
citation_txt	Superfluidity of a condensate with np pairing correlations in asymmetric nuclear matter / A.I. Akhiezer, A.A. Isayev, S.V. Peletminsky, A.A. Yatsenko // Вопросы атомной науки и техники. — 2001. — № 6. — С. 334-338. — Бібліогр.: 13 назв. — англ.
series	Вопросы атомной науки и техники
work_keys_str_mv	AT akhiezerai superfluidityofacondensatewithnppairingcorrelationsinasymmetricnuclearmatter AT isayevaa superfluidityofacondensatewithnppairingcorrelationsinasymmetricnuclearmatter AT peletminskysv superfluidityofacondensatewithnppairingcorrelationsinasymmetricnuclearmatter AT yatsenkoaa superfluidityofacondensatewithnppairingcorrelationsinasymmetricnuclearmatter
first_indexed	2025-07-06T03:59:00Z
last_indexed	2025-07-06T03:59:00Z
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fulltext	Q U A N T U M F L U I D S SUPERFLUIDITY OF A CONDENSATE WITH np PAIRING CORRELA- TIONS IN ASYMMETRIC NUCLEAR MATTER A.I. Akhiezer, A.A. Isayev, S.V. Peletminsky, A.A. Yatsenko National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine Influence of asymmetry on superfluidity of nuclear matter with triplet-singlet pairing of nucleons (in spin and isospin spaces) is considered within the framework of a Fermi-liquid theory. Solutions of self-consistent equations for the energy gap at 0=T are obtained. It is shown, that if the chemical potentials of protons and neutrons are de- termined in the zero gap width approximation, then the energy gap for some values of density and asymmetry param- eter of nuclear matter demonstrates double-valued behavior. However, with account for the feedback of pairing cor- relations through the normal distribution functions of nucleons two-valued behavior of the energy gap turns into uni- versal one-valued behavior. At 0=T the energy gap has a discontinuities as a function of density in a narrow layer model. These discontinuities depend on the asymmetry parameter. PACS: 21.65.+f; 21.30.Fe; 71.10.Ay 1. GENERAL EQUATIONS OF THE THE- ORY It is well established, that neutron-proton (np) pair- ing plays an essential role in description of superfluidity of finite nuclei with N=Z (see Ref. [1] and references therein) and symmetric nuclear matter [2-4]. In this re- port we shall investigate influence of asymmetry on np superfluidity of nuclear matter. Earlier this problem was treated with the use of various approaches and potentials of NN interaction. In particular, the cases of 3S1-3D1 and 3D2 pairing were considered in Refs. [2,5] on the base of the Thouless criterion for the thermodynamic T matrix. As a potential of NN interaction, the Graz II and Paris potential were chosen respectively. Superfluidity in 3S1- 3D1 pairing channel was studied also in Ref. [6] within BCS theory of superconductivity with the use of the Paris potential in the separable form. Investigations, based on the Thouless criterion, deduce the suppression of np pairing correlations with increase of isospin asym- metry. However, the Thouless criterion can be exploited for finding the critical temperature only, but does not permit to draw any conclusions about superfluidity with a finite gap. The studies in Ref. [6], based on the BCS theory, were carried out with the use of the bare interac- tion and the single particle spectrum of a free Fermi gas and give, thus, overestimated values of the energy gap. The effect of ladder-renormalized single particle spec- trum on the magnitude of the energy gap in 3S1-3D1 pair- ing channel was investigated in Ref. [7]. The Argonne V14 potential was explored as input for determination of the single particle energy and the bare interaction in the form of the Paris potential was used to evaluate the ener- gy gap. The use of the bare interaction in the gap equa- tion seems to be a very strong simplification, because medium polarization strongly reduces the magnitude of the gap. In principle, the effective pairing interaction should be obtained by means of Brueckner renormaliza- tion, which gives the correct interaction after modifying the bare interaction for the effect of nuclear medium. However, the issue of microscopic many-body calcula- tion of the effective pairing potential is a complex one and still is not solved. For this reason, it is quite natural step to develop some kind of a phenomenological theo- ry, where instead of microscopical calculation of the pairing interaction one exploits the phenomenological effective interaction. We shall investigate influence of asymmetry on superfluid properties of nuclear matter, using Landau's semiphenomenological theory of a Fer- mi-liquid (FL). In the Fermi-liquid model the normal and anomalous FL interaction amplitudes are taken into account on an equal footing. This will allow us to con- sider consistently influence of the FL amplitudes on su- perfluid properties of nuclear matter. Besides, as a po- tential of NN interaction we choose the Skyrme effec- tive forces, describing interaction of two nucleons in the presence of nucleon medium. The Skyrme forces are widely used in description of nuclear system properties and, in particular, they were exploited for description of superfluid properties of finite nuclei [8,9] as well as infi- nite symmetric nuclear matter [10-12]. The basic formalism is laid out in more detail in Ref. [11], where superfluidity of symmetric nuclear matter was studied. As shown there, superfluidity with triplet- singlet (TS) pairing of nucleons (total spin S and isospin T of a pair are equal 1=S , 0=T ) is realized near the saturation density in symmetric nuclear matter with the Skyrme interaction. Therefore, further we shall study in- fluence of asymmetry on superfluid properties of TS phase of nuclear matter. For the states with the projec- tions of total spin and isospin 0== zz TS , the normal distribution function f and the anomalous distribution function g have the form 30030000 )()()( τστσ pfpfpf  += , (1) 22330 )()( τσσpgpg  = , where iσ and kτ are the Pauli matrices in spin and isospin spaces. The operator of quasiparticle energy ε and the matrix order parameter ∆ of the system for the energy functional, being invariant with respect to rota- 78 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2001, № 6, p. 334-338. tions in spin and isospin spaces, have the analogous structure: 30030000 )()()( τσετσεε ppp  += , (2) 22330 )()( τσσpp  ∆=∆ . Using the minimum principle of the thermodynamic potential and procedure of block diagonalization [13], one can express evidently the distribution functions 300300 ,, gff in terms of the quantities ε and ∆ :      − + + −= T E T E E f 2 tanh 2 tanh 42 1 030300 00 ξξξ , (3)      −−+−= T E T Ef 2 tanh 2 tanh 4 1 0303 03 ξξ , (4)      − + +∆ −= T E T E E g 2 tanh 2 tanh 4 030330 30 ξξ . (5) Here 2 30 2 00 ∆+= ξE , 0 000000 µεξ −= , 0 030303 µεξ −= , 2 00 0 00 np µµ µ + = , 2 00 0 03 np µµ µ − = , T is temperature, 0 pµ and 0 nµ are chemical potentials of protons and neutrons. To obtain the closed system of equations for the quasiparticle energy ε and ∆ , it is necessary to express the quantities ε and ∆ through the distribution functions f and g. For this purpose one has to set the energy functional ),( gfE of the system. In the case of asymmetric nuclear matter with TS pairing of nucleons the energy functional is characterized by two normal 20 ,UU and one anomalous 1V FL ampli- tudes [11]. Differentiating the functional E(f,g) with re- spect to g [13] and using Eq. (5), one can obtain the gap equation in the form ∑ ∆ −=∆ q qE q qpV V p )( )( ),( 4 1)( 30 130          − + + × T E T E 2 tanh 2 tanh 0303 ξξ (6) The anomalous interaction amplitude 1V in the Skyrme model reads [11] )1( 6 1)1(),( 33001 xtxtqpV +++= βρ  (7) ),)(1( 2 1 22 112 qpxt   +++ where ρ is density of nuclear matter, it , ix , β are some phenomenological parameters, which differ for various versions of the Skyrme forces (later we shall use the SkP potential [8,14]). Eq. (6) should be solved joint- ly with equations ∑       + − p T ppE pE p V 2 )()( tanh )( )( 21 0300    ξξ ρ ξ =      − + T ppE 2 )()( tanh 03  , (8) α ρ ξξ =       − − +∑ p T E T E V 2 tanh 2 tanh1 0303 (9) being the normalization conditions for the normal distri- bution functions 0300 , ff . In Eq. (9) the quantity ρρρα /)( pn −= is the asymmetry parameter of nucle- ar matter, np ρρ , are the partial number densities of protons and neutrons. Note that account of the normal FL amplitudes in the case of the effective Skyrme inter- action, being quadratic in momenta, is reduced to renor- malization of free nucleon masses and chemical poten- tials. Expressions for the quantities 0300 , ξξ , which enter in Eqs. (6,8,9), with regard for the explicit form of the amplitudes 20 ,UU [11] read 00 00 2 00 2 µξ −= m p , 03 03 2 03 2 µξ −= m p , where the effective nucleon mass 00m and effective isovector mass 03m are defined by the formulas [ ])45(3 1622 2210 00 2 00 2 xtt mm +++= ρ , (10) [ ])21()21( 162 2211 03 2 xtxt m +−+= α ρ , 0 00m being the bare mass of a nucleon. The renormalized chemical potentials 0300 , µµ should be determined from Eqs. (8,9) and in the leading approximation on the ratios FT ε/ , Fε/∆ have the form )( 2 1 00 np µµµ += , )( 2 1 03 np µµµ −= , (11) np F np m k np , 22 , 2 ,  =µ where 3/1 , 2 )3( , npF np k ρπ= , pm and nm are the proton and neutron effective masses, defined as np mmm 112 00 += , np mmm 112 03 −= . The proton and neutron effective masses, according to Eqs. (10), can be written in the form β+ = 1 00m m p , β− = 1 00m mn , (12) rα ρβ = , =r [ ] [ ])45(38 )21()21( 221 0 00 2 2211 0 00 xttm xtxtm +++ +−+ ρ . 79 In Eq. (12) the dependence on the asymmetry param- eter α is contained through the quantity β . With ac- count of Eqs. (11,12) for the renormalized chemical po- tentials 0300 , µµ we obtain ( ) ( ) ( ) ( ){ }βαβαµµ −+++−= 1111 2 3/23/20 00 , (13) ( ) ( ) ( ) ( ){ }βαβαµµ −+−+−= 1111 2 3/23/20 03 , 3/22 00 2 0 2 3 2     ≡ ρπµ m  . 2. ENERGY GAP AT ZERO TEMPERATURE We write now the self-consistent equations for deter- mining the energy gap and effective chemical potentials at 0=T . Considering, that the interaction amplitude 1V is not equal to zero only in a narrow layer near the Fer- mi-surface, 000 θξ ≤ (we shall set 000 1.0 µθ = ) and en- tering new dimensionless variables 0000 µξξ = , 0030 µ∆=∆ , 00033 µξξ = , we present these equations in the form [ ]∫− −++= θ θ ξξξ )sgn()sgn( 4 1 33 EE E dg (14) ∫ ∞ − + 1 00 1 ξξµν dF (15) [ ] ρξξξ =       −++−× )sgn()sgn(2 33 EE E , [ ] α ρξξξξµν =−−++∫ ∞ − )sgn()sgn(1 33 1 00 EEdF .(16) Here 22 ∆+= ξE , ),(1 FFF pqppVg ==−= ν , 32 00 2 π ν f F pm = , 00002 µmpF = , and 000 µθθ = is dimensionless cut-off parameter. For 0>α it holds 003 >m , 003 <µ , and, hence )sgn(1)sgn()sgn( 2 3 2 33 ξξξ −+=−++ EEE , )sgn(1)sgn()sgn( 2 3 2 33 ξξξ −−=−−+ EEE . The contribution to the gap equation (14) gives the domain on ξ , for which the expression 2 3 2 ξ−E is posi- tive. Its roots are equal 2222 ∆−±=± γϕβ ϕξγ . Here 00 03 03 00 µ µ ϕ −= m m , 22 1 βγ −= . If 222 ∆< γϕ , then 1)sgn( 2 3 2 =− ξE and, hence, the whole domain from θ− to θ gives the contribution to the integral in Eq. (14). In this case we arrive at the equation of the BCS type at 0=T with the solution )1sinh(/ gθ=∆ . Eqs. (14)-(16) can be solved in two approximations: when one disregards by the dependence from ∆ in chemical potentials 0300 , µµ and when this dependence is taken into account exactly. First, we con- sider the former case. Using Eqs. (15,16), it is easy to see that the quantity ϕ in the main approximation on the ratio Fε/∆ and 1< <α reads )( 3 2 3ααϕ O+= Thus, at α3 2≡∆≥∆ c we arrive at the BCS solution at 0=T . If c∆<∆ , the gap equation reads ++ −− +∆+ +∆+ ⋅ −∆+ +∆+ = ξξ θθ θθ ξξ 22 22 22 22 ln 2 1 g , (17) 22 ∆−∆±≈± cξ , assuming that 1< <α and quantities ±ξ lye in the inter- val ),( θθ− . Solution of Eq. (17) can be presented in the form (for c∆<∆ ) ( )( )cc ∆+−∆ + =∆ λ θθλ λ λ 22 2 )1( 4 , )1exp( g=λ . (18) For the densities where θλ <∆ c , we have 0≡∆ . Thus, in the zero gap size approximation in chemical poten- tials we have two solutions for the energy gap: one solu- tion corresponds to BCS solution at c∆≥∆ and the sec- ond one is described by Eq. (18). Now we present the results of numerical integration of the gap equation for the given case (Fig. 1). In the case of symmetric nuclear matter ( 0=α ) we obtain the phase curve with one-valued behavior of the gap. For small values of asymmetry α there exist such regions of large and low densities of nuclear matter (ex- cluding some vicinity of the point 0=ρ ), for which we have two values of the energy gap, where one of these values is the solution of the BCS type and practically co- incides with the corresponding value of the gap for the case 0=α . When α increases, these regions begin to approach and at some value cαα = it takes place conti- guity of the regions with two solutions. For cαα > two branches of the phase curves are separated ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2000, №2. Серия: Ядерно-физические исследования (36), с. 3-6. 80 0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.0 0.5 1.0 1.5 2.0 SkP α =0 α =0.06 α =0.07 α =0.072 α =0.09 α =0.14 ∆ (M eV ) ρ (fm-3) Fig. 1. Energy gap as a function of density in un- coupled calculations from the density axis and combine to one curve, begin- ning and ending in some points of the phase curve with 0=α . When α increases further, these points move to- wards and at some mαα = the branches of solutions contract to a point. The value mα determines the maxi- mum value of the asymmetry parameter, when TS super- fluidity exists at 0=T ( 179.0≈α m ). To find this value, let us denote as λ the mini- mum value of the parameter λ , corresponding to the maximum value g of the coupling constant. The val- ue mα is found from the relationship cBCS ∆=∆  , whence we get . 1 3 2 min min −λ θλ=α m The position of the boundary points  ρρ , , limiting the interval, where solutions exist, is determined from the requirement cBCS ∆=∆ , from here we ob- tain the equation c c ∆ ∆++ = 22 )( θθ ρλ . The points maxmin , ρρ ′′ , at which the gap vanishes, are found from the relationship c∆ = θρλ )( . For cα λ θα ≡> min2 3 the points maxmin , ρρ ′′ are absent, and, hence, for the lower branch c∆≤∆<0 . At cαα = we have maxmin ρρ ′=′ . All these peculiarities are qualita- tively seen from Fig. 2. 0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.00 0.03 0.06 0.09 0.12 0.15 α =0 α =0.06 α =0.07 α =0.072 α =0.09 α =0.14 SkP ∆/ ε F ρ (fm-3) Fig. 2. The ratio Fε30∆ as a function of density in uncoupled calculations Let us find now the solutions of Eqs. (14-16) with account for the influence of the finite size of the gap on the chemical potentials µ00, µ03. Calculations show, that in self-consistent treatment of Eqs. (14-16) it will be re- alized only the case 0222 <γ∆−ϕ , and, hence, we have only solution of the BCS type. Since 0222 <γ∆−ϕ , Eq. (16) will have nontrivial solu- tion for the chemical potential 03µ , if the roots )0(0 =∆≡ ±± ξξ of the subintegrand function at 0=∆ will be located outside the interval ( θθ− , ). The results of self-consistent integration of the gap equation are presented in Fig. 3. 0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.0 0.5 1.0 1.5 2.0 SkP ∆ (M eV ) ρ (fm-3) α =0.0001 α =0.01 α =0.02 α =0.026 Fig. 3. Energy gap as a function of density in self-con- sistent scheme Here the dashed lines are drawn through the boundary points of the curves, being the solutions of Eqs. (14-16) for different α . One can see, that taking into account the feedback of the finite size of the gap through the normal distribution functions 0300 , ff in Eqs. (3,4), leads to the qualitative change: instead of two-valued behavior of the gap we have universal one-valued be- 81 havior. The first solution of the BCS type, obtained in uncoupled calculation, remains practically unchanged in self-consistent treatment of the gap equation (14) and with sufficiently high accuracy equals to its value in the self-consistent determination. The second solution in un- coupled scheme, to which corresponds the smaller gap width, tends to the first solution of the BCS type under simultaneous iterations of Eqs. (14,16). Taking into ac- count the finiteness of the gap results in reduction of the threshold asymmetry, at which superfluidity disappears, to the value 03.0≈mα . Thus, in spite of the smallness of the ratio Fε∆ for all densities ρ , the backward in- fluence of pairing correlations is significant. This is ex- plained by the fact, that if the quantity ∆ in Eqs. (15,16) differs from zero, then the absolute value of the chemi- cal potential 03µ increases a few times as against its value at 0=∆ . The increase of 03µ is equivalent to the increase of the effective shift between neutron and proton Fermi surfaces that leads to significant reduction of the threshold asymmetry. Note, that in a narrow layer model the gap is everywhere finite as a function of den- sity. In summary, we studied TS superfluidity of asym- metric nuclear matter in FL model with density-depen- dent Skyrme effective interaction (SkP force). In FL ap- proach the normal and anomalous FL amplitudes are taken into account on an equal footing and this allows to consider consistently within the framework of a phe- nomenological theory the influence of medium effects on superfluid properties of nuclear matter. It is shown, that in the case, when the chemical potentials 0300 , µµ (half of a sum and half of a difference of the proton and neutron chemical potentials, respectively) are deter- mined in the approximation of ideal Fermi-gas, the ener- gy gap demonstrates for some values of density and asymmetry parameter the double-valued behavior. If to consider the feedback of pairing correlations through the dependence of the normal distribution functions of nu- cleons from the energy gap, then the energy gap drasti- cally changes its behavior from two-valued to universal one-valued character. In spite of relative smallness of the ratio Fε∆ , taking into account of the finite size of the gap in chemical potentials leads to the significant in- crease of absolute value of 03µ and, hence, to consider- able reduction of the threshold asymmetry, at which su- perfluidity at T=0 disappears. In self-consistent determi- nation the energy gap at T=0 as a function of density has a finite width. Among the other problems we note here the study of multi-gap superfluidity [12] in asymmetric nuclear matter. ACKNOWLEDGMENTS Authors thank A. Sedrakian for valuable comment. The financial support of STCU (grant №1480) is ac- knowledged. REFERENCES 1. G. Roepke, A. Schnell, P. Schuck, and U. Lombardo. Isospin singlet (pn) pairing and quar- tetting contribution to the binding energy of nuclei // Phys. Rev. C. 2000, v. 61, 024306. 2. Th. Alm, B.L. Friman, G. Roepke, and H.J. Schulz. Pairing instability in hot asymmetric nuclear matter // Nucl. Phys. 1993, v. A551, p. 45- 53. 3. M. Baldo, U. Lombardo, and P. Schuck. Deuteron formation in expanding nuclear matter from a strong coupling BCS approach // Phys. Rev. C. 1995, v. 52, p. 975-985. 4. E. Garrido, P. Sarriguren, E. Moya de Guer- ra, and P. Schuck. Effective density dependent pairing forces in the T=1 and T=0 channels // Phys. Rev. C. 1999, v. 60, 064312. 5. Th. Alm, G. Roepke, A. Sedrakian, and F. Weber. 3D2 pairing in asymmetric nuclear matter // Nucl. Phys. 1996, v. A604, p. 491-504. 6. A. Sedrakian, T. Alm, and U. Lombardo. Su- perfluidity in asymmetric nuclear matter // Phys. Rev. C. 1997, v. 55, R582-R584. 7. A. Sedrakian and U. Lombardo. Thermody- namics of a n-p condensate in asymmetric nuclear matter // Phys. Rev. Lett. 2000, v. 84, 602-605. 8. J. Dobaczewski, H. Flocard, and J. Treiner. Hartree-Fock-Bogolyubov description of nuclei near the neutron-drip line // Nucl. Phys. 1984, v. A422, 103-139. 9. P.-G. Reinhard, D.J. Dean, W. Nazarewicz, et al. Shape coexistence and the effective nucleon- nucleon interaction // Phys. Rev. C. 1999, v. 60, 014316; R.K. Su, S.D. Yang, and T.T.S. Kuo. Liq- uid-gas and superconducting phase transitions of nuclear matter, calculated with real time Green’s function methods and Skyrme interactions // Phys. Rev. C. 1987, v. 35, p. 1539-1550. 10. A.I. Akhiezer, A.A. Isayev, S.V. Peletmin- sky, A.P. Rekalo, and A.A. Yatsenko. On a theory of superfluidity of nuclear matter based on the Fer- mi-liquid approach // Zh. Eksp. Teor. Fiz. 1997, v. 112, p. 3-24 [Sov. Phys. JETP 1997, v. 85, p. 1]. 11. A.I. Akhiezer, A.A. Isayev, S.V. Peletmin- sky, and A.A. Yatsenko. Multi-gap superfluidity in nuclear matter. // Phys. Lett. B. 1999, v. 451, p. 430-436. 12. A.I. Akhiezer, V.V. Krasil'nikov, S.V. Peletminsky, and A.A. Yatsenko. Research on superfluidity and superconductivity on the basis of the Fermi-liquid concept // Phys. Rep. 1994, v.245, p. 3-110. 13. M. Brack, C. Guet and H.-B. Hakansson. Self-consistent semiclassical description of average nuclear properties – a link between microscopic and macroscopic models // Phys. Rep. 1985, v. 123, p. 275-364. ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2000, №2. Серия: Ядерно-физические исследования (36), с. 3-6. 82 A.I. Akhiezer, A.A. Isayev, S.V. Peletminsky, A.A. Yatsenko National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine 1. GENERAL Equations OF THE THEORY 2. ENERGY GAP AT ZERO TEMPERATURE acknowledgmentS REFERENCES

Superfluidity of a condensate with np pairing correlations in asymmetric nuclear matter

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