Exact solution of Dirac equation for Scarf potential with new tensor coupling potential for spin and pseudospin symmetries using Romanovski polynomials

doi:10.1088/1674-1056/23/9/090304

›› 2014, Vol. 23 ›› Issue (9): 90304-090304.doi: 10.1088/1674-1056/23/9/090304

Exact solution of Dirac equation for Scarf potential with new tensor coupling potential for spin and pseudospin symmetries using Romanovski polynomials

A. Suparmi^a, C. Cari^a, U. A. Deta^b

a Physics Department, Faculty of Mathematics and Natural Science, Sebelas Maret University, Indonesia;
b Department of Physics, Faculty of Mathematics and Natural Science, State University of Surabaya, Indonesia

收稿日期:2014-02-07 修回日期:2014-04-02 出版日期:2014-09-15 发布日期:2014-09-15
基金资助:
Project supported by Hibah Peneliti Utama (PUT UNS) 2014 and DIKTI (Grant No. 165a/UN27.11/PN2013).

Exact solution of Dirac equation for Scarf potential with new tensor coupling potential for spin and pseudospin symmetries using Romanovski polynomials

A. Suparmi^a, C. Cari^a, U. A. Deta^b

a Physics Department, Faculty of Mathematics and Natural Science, Sebelas Maret University, Indonesia;
b Department of Physics, Faculty of Mathematics and Natural Science, State University of Surabaya, Indonesia

Received:2014-02-07 Revised:2014-04-02 Online:2014-09-15 Published:2014-09-15
Contact: A. Suparmi E-mail:suparmi@uns.ac.id
Supported by:
Project supported by Hibah Peneliti Utama (PUT UNS) 2014 and DIKTI (Grant No. 165a/UN27.11/PN2013).

摘要/Abstract

摘要： The bound state solutions of Dirac equations for a trigonometric Scarf potential with a new tensor potential under spin and pseudospin symmetry limits are investigated using Romanovski polynomials. The proposed new tensor potential is inspired by superpotential form in supersymmetric (SUSY) quantum mechanics. The Dirac equations with trigonometric Scarf potential coupled by a new tensor potential for the pseudospin and spin symmetries reduce to Schrödinger-type equations with a shape invariant potential since the proposed new tensor potential is similar to the superpotential of trigonometric Scarf potential. The relativistic wave functions are exactly obtained in terms of Romanovski polynomials and the relativistic energy equations are also exactly obtained in the approximation scheme of centrifugal term. The new tensor potential removes the degeneracies both for pseudospin and spin symmetries.

关键词: Scarf potential, new tensor potential, spin and pseudospin symmetries, Romanovski polynomials

Abstract: The bound state solutions of Dirac equations for a trigonometric Scarf potential with a new tensor potential under spin and pseudospin symmetry limits are investigated using Romanovski polynomials. The proposed new tensor potential is inspired by superpotential form in supersymmetric (SUSY) quantum mechanics. The Dirac equations with trigonometric Scarf potential coupled by a new tensor potential for the pseudospin and spin symmetries reduce to Schrödinger-type equations with a shape invariant potential since the proposed new tensor potential is similar to the superpotential of trigonometric Scarf potential. The relativistic wave functions are exactly obtained in terms of Romanovski polynomials and the relativistic energy equations are also exactly obtained in the approximation scheme of centrifugal term. The new tensor potential removes the degeneracies both for pseudospin and spin symmetries.

Key words: Scarf potential, new tensor potential, spin and pseudospin symmetries, Romanovski polynomials

中图分类号: (Solutions of wave equations: bound states)

03.65.Ge

03.65.Pm (Relativistic wave equations) 03.65.Ca (Formalism)

A. Suparmi, C. Cari, U. A. Deta. Exact solution of Dirac equation for Scarf potential with new tensor coupling potential for spin and pseudospin symmetries using Romanovski polynomials[J]. , 2014, 23(9): 90304-090304.

参考文献 58

[1]	Alberto P, Lisboa R, Malheiro M and De Castro A S 2005 Phys. Rev. C 71 034313
[2]	Zhang L H, Li X P and Jia C S 2008 Phys. Lett. A 372 2201
[3]	Wei G F and Dong S H 2008 Phys. Lett. A 373 49
[4]	Ikhdair S M and Hamzavi M 2013 Chin. Phys. B 22 090305
[5]	Ikhdair S M and Sever R 2010 Appl. Math. Comput. 216 911
[6]	Hamzavi M, Rajabi A A and Hassanabadi H 2010 Phys. Lett. A 374 4303
[7]	Wei G F and Dong S H 2008 Phys. Lett. A 373 49
[8]	Xu Y, He S and Jia C S 2008 J. Phys. A: Math. Theory 41 0255302
[9]	Hamzavi M and Rajabi A A 2013 Adv. High. Energy Phys. 2003 196986
[10]	Ikhdair S M and Sever R 2010 arXiv:1001.4327v2 [math-ph]
[11]	Ikot A N 2013 Commun. Theor. Phys. 59 268
[12]	Aydogdu O, Maghsoodhi E and Hassanabadi H 2013 Chin. Phys. B 22 010302
[13]	Zhou F, Wu Y and Guo J Y 2009 Commun. Theor. Phys. 52 813
[14]	Ping Z A and Chao W 2007 High Energy Phys. Nucl. Phys. 31 1027
[15]	Chen G 2004 Phys. Lett. A 328 116
[16]	Chen G, Chen Z D and Lou Z M 2004 Chin. Phys. 13 279
[17]	Guo J Y, Zhou F, Gou F L and Zhou J H 2007 Int. J. Mod. Phys. A 22 4825
[18]	Chen C H 2005 Phys. Lett. A 339 283
[19]	Aydogdu O and Sever R 2011 Phys. Lett. B 703 379
[20]	Chen G 2004 Mod. Phys. Lett. A 19 2009
[21]	Yan Z and Gou J Y 2008 Chin. Phys. B 17 0380
[22]	Hu X Q, Luo G, Wu Z M, Niu L B and Ma Y 2010 Commun. Theor. Phys. 53 242
[23]	Soylu A, Bayrak O and Boztosun I 2007 J. Math. Phys. 48 082302
[24]	Bahar M K and Yasuk F 2013 Chin. Phys. B 22 010301
[25]	Greene R L and Aldrich C 1976 Phys. Rev. A 14 2363
[26]	Hecht K T and Adler A 1969 Nucl. Phys. A 137 129
[27]	Arima, A, Harvey M and Shimizu K 1969 Phys. Lett. B 30 517
[28]	Ginocchio J N 2004 Phys. Rep. C 69 034318
[29]	Ginocchio J N 1997 Phys. Rev. Lett. 78 436
[30]	Meng J, Sugaware-Tanabe K, Yamaji S and Arima A 1999 Phys. Rev. C 59 154
[31]	Dudek J, Nazarewicz W, Szymanski Z and Leander G A 1987 Phys. Rev. Lett. 59 1405
[32]	Troltenier D, Bahri C and Draayer J P 1995 Nucl. Phys. A 586 53
[33]	Page P R, Goldman T and Ginocchio J N 2001 Phys. Rev. Lett. 86 204
[34]	Ginocchio J N 2005 Phys. Rep. 414 165
[35]	Gouppert-Mayer M 1949 Phys. Rev. 75 1969
[36]	Li D P, Chen S W and Guo J Y 2013 arXiv:1304.0320v1 [nucl-th]
[37]	Ginocchio J N and Madland D G 1998 Phys. Rev. C 57 1167
[38]	Alberto P, Fiolhais M, Malheiro M, Delfino A and Chiapparini M 2002 Phys. Rev. C 65 034307
[39]	Troltenier D, Nazarewicz W, Szymanski Z and Draayer J P 1994 Nucl. Phys. A 567 591
[40]	Stuchbery A E 2002 Nucl. Phys. A 700 83
[41]	Liu Q, Niu Z M and Guo J Y 2014 Phys. Rev. A 87 052122
[42]	Guo J Y 2012 Phys. Rev. C 85 021302 (R)
[43]	Guo J Y, Chen S W, Niu Z M and Li D P 2014 Phys. Rev. Lett. 112 062502
[44]	Guo J Y, Chen S W, Niu Z M, Li D P and Liu Q 2013 arXiv: 1309.1523v1 [nucl-th]
[45]	Aydogdu O and Sever R 2010 Few-Body Syst. 47 193
[46]	Akcay H 2009 Phys. Lett. 373 616
[47]	Hamzavi M, Rajabi A A and Hassanabadi H 2010 Few-Body Syst. 48 171
[48]	Koepf W and Masjed-Jamei M 2006 Integral Transform and Special Functions 17 559
[49]	Routh E J 1884 Proc. London Math. Soc. s1-16 245
[50]	Romanovski V I 1929 Compt. Rend. Acad. Sci. Paris 188 1023
[51]	Alvarez-Castillo D E and Kirbach M 2007 Rev. Mex. Fis. E 53 143
[52]	Raposo A, Weber H J, Alvarez-Castillo D E and Kirchbach M 2007 Eur. Phys. J. 5 253
[53]	Alvarez-Castillo D E, Compean C B and Kirbach M 2011 arXiv: 1105. 1354v1[quant-ph]
[54]	Cari C, Suparmi A, Deta U A and Werdiningsih I S 2013 Makara J. Sci. 17 3
[55]	Suparmi A, Cari C and Handhika J 2013 J. Phys Conf. Ser. 423 012039
[56]	Cari C and Suparmi A 2013 J. Phys. Conf. Ser. 423 012031
[57]	Suparmi A and Cari C 2013 At. Ind. J. 39 3
[58]	Nikiforov A F and Uvarov V B 1988 Special Functions of Mathematical Physics (Birkhauser Verlag Basel) p. 1

Exact solution of Dirac equation for Scarf potential with new tensor coupling potential for spin and pseudospin symmetries using Romanovski polynomials

Exact solution of Dirac equation for Scarf potential with new tensor coupling potential for spin and pseudospin symmetries using Romanovski polynomials

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