Influence of isovector pairing and particle-number projection effects on spectroscopic factors for one-pair like-particle transfer reactions in proton-rich even-even nuclei

Y. Benbouzid; N. H. Allal; M. Fellah; M. R. Oudih

doi:10.1088/1674-1137/42/4/044103

Chinese Physics C> 2018, Vol. 42> Issue(4) : 044103 DOI: 10.1088/1674-1137/42/4/044103

Influence of isovector pairing and particle-number projection effects on spectroscopic factors for one-pair like-particle transfer reactions in proton-rich even-even nuclei

Abstract
HTML
Reference
Related

PDF

Abstract：
Isovector neutron-proton (np) pairing and particle-number fluctuation effects on the spectroscopic factors (SF) corresponding to one-pair like-particle transfer reactions in proton-rich even-even nuclei are studied. With this aim, expressions of the SF corresponding to two-neutron stripping and two-proton pick-up reactions, which take into account the isovector np pairing effect, are established within the generalized BCS approach, using a schematic definition proposed by Chasman. Expressions of the same SF which strictly conserve the particle number are also established within the Sharp-BCS (SBCS) discrete projection method. In both cases, it is shown that these expressions generalize those obtained when only the pairing between like particles is considered. First, the formalism is tested within the Richardson schematic model. Second, it is applied to study even-even proton-rich nuclei using the single-particle energies of a Woods-Saxon mean-field. In both cases, it is shown that the np pairing effect and the particle-number projection effect on the SF values are important, particularly in N=Z nuclei, and must then be taken into account.
- neutron-proton pairing ,
- particle-number fluctuations ,
- spectroscopic factor

References

[1]	B. Blank and M. J. G. Borge, Progr. Part. Nucl. Phys., 60:403-483 (2008)
[2]	M. Pfutzner, M. Karny, L. V. Grigorenko et al, Rev. Mod. Phys., 84:567-619 (2012)
[3]	H. Sagawa and K. Hagino, Eur. Phys. J. A, 51:102 (2015)
[4]	T. Nakamura, H. Sakurai, and H. Watanabe, Progr. Part. Nucl. Phys., 97:53-122 (2017)
[5]	A. L. Goodman, Adv. Nucl. Phys., 11:263-366 (1979)
[6]	J. Engel, S. Pittel, M. Stoitsov et al, Phys. Rev. C, 55:1781-1788 (1997)
[7]	O. Civitarese and M. Reboiro, Phys. Rev. C, 56:1179-1182 (1997)
[8]	A. A. Raduta, L. Pacearescu, P. Sarriguren et al, Nucl. Phys. A, 675:503-530 (2000)
[9]	F. Simkovic, Ch. C. Moustakidis, L. Pacearescu et al, Phys. Rev. C, 68:054319 (2003)
[10]	N. Sandulescu, D. Negrea, J. Dukelsky et al, Phys. Rev. C, 85:061303 (R) (2012)
[11]	H. Sagawa, Y. Tanimura, and K. Hagino, Phys. Rev. C, 87:034310 (2013)
[12]	N. Hinohara and J. Engel, Phys. Rev. C, 90:031301 (R) (2014)
[13]	M. Sambataro and N. Sandulescu, Phys. Rev. C, 93:054320 (2016)
[14]	Wenjin Tan, Dongdong Ni, and Zhongzhou Ren, Chin. Phys. C, 41:54103 (2017)
[15]	P. Van Isacker, J. Engel, and K. Nomura, arXiv:1708.05925.
[16]	S. Frauendorf and A. O. Machiavelli, Prog. Part. Nucl. Phys., 78:24-90 (2014)
[17]	C. Qi and R. Wyss, Phys. Scr., 91:013009 (2016)
[18]	J. Bardeen, L. N. Cooper and J. R. Schriefier, Phys. Rev., 106:162-164 (1957)
[19]	A. Goswami, Nucl. Phys., 60:228-240 (1964)
[20]	A. Goswami and L. S. Kisslinger, Phys. Rev., 140:B26-B31 (1965)
[21]	H. T. Chen and A. Goswami, Nucl. Phys., 88:208-214 (1966)
[22]	H. Chen and A. Goswami, Phys. Lett. B, 24:257-259 (1967)
[23]	G. G. Dussel, E. Maqueda and R. P. J. Perazzo, Nucl. Phys. A, 153:469-480 (1970)
[24]	H. H. Wolter, A. Faessler and P. U. Sauer, Nucl. Phys. A, 167:108-128 (1971)
[25]	A. L. Goodman, Nucl. Phys. A, 186:475-492 (1972)
[26]	O. Civitarese, M. Reboiro and P. Vogel, Phys. Rev. C, 56:1840-1843 (1997)
[27]	D. Mokhtari, N. H. Allal and M. Fellah, Acta Phys. Hung. A:Heavy Ion Phys., 19:187-190 (2004)
[28]	D. Mokhtari, M. Fellah and N. H. Allal, Int. J. Mod. Phys. E, 25:1650035 (2016)
[29]	P. Ring and P. Schuck, The Nuclear Many Body Problem, (Berlin, Springer, 1980)
[30]	J. Dukelsky, S. Pittel and C. Esebbag, Phys. Rev. C, 93:034313 (2016)
[31]	N. H. Allal and M. Fellah, Phys. Rev. C, 43:2648-2657 (1991)
[32]	N. H. Allal, M. Fellah, N. Benhamouda et al, Phys. Rev. C, 77:054310 (2008)
[33]	Faiza Hammache, N. H. Allal, M. Fellah et al, Int. J. Mod. Phys. E, 25:1650032 (2016)
[34]	N. Benhamouda, N. H. Allal, M. Fellah et al, Int. J. Mod. Phys. E, 17:1357-1365 (2008)
[35]	S. Kerrouchi, D. Mokhtari, N. H. Allal et al, Int. J. Mod. Phys. E, 18:141-160 (2009)
[36]	M. Douici, N. H. Allal, M. Fellah, et al, Int. J. Mod. Phys. E, 21:1250046 (2012)
[37]	N. H. Allal, M. Fellah, M. Douici et al, Int. J. Mod. Phys. E, 25:1650108 (2016)
[38]	M. Douici, N.H. Allal, M. Fellah, et al, Int. J. Mod. Phys. E, 22:1350029 (2013)
[39]	M. Borrajo and J. L. Egido, Phys. Lett. B, 764:328-334 (2017)
[40]	D. C. Zheng, D. W. L. Sprung and H. Flocard, Phys. Rev. C, 46:1355-1363 (1992)
[41]	J. A. Sheikh, P. Ring, E. Lopes et al, Phys. Rev. C 66:044318 (2002)
[42]	G. Hupin and Denis Lacroix, Phys. Rev. C, 86:024309 (2012)
[43]	S. Kerrouchi, N. H. Allal, M. Fellah et al, Int. J. Mod. Phys. E, 19:1383-1409 (2010)
[44]	S. Kerrouchi, N. H. Allal, M. Fellah et al, Int. J. Mod. Phys. E, 24:1550014 (2015)
[45]	H. J. Lipkin, Ann. Phys. (NY), 12:452-462 (1960)
[46]	Y. Nogami, Phys. Rev., 134, B313-B321 (1964)
[47]	W. Satula and R. Wyss, Phys. Lett. B, 393:1-6 (1997)
[48]	W. Satula and R. Wyss, Nucl. Phys. A, 676:120-142 (2000)
[49]	K. Sieja and A. Baran, Acta Phys. Pol. B, 35:107-114 (2006)
[50]	V. N. Fomenko, J. Phys A, 3:8-20 (1970)
[51]	M. Fellah, T. F. Hammann, and D. E. Medjadi, Phys. Rev. C, 8:1585-1592 (1973)
[52]	M. Fellah and T. F. Hammann, Phys. Rev. C, 20:1560-1571 (1979)
[53]	N. H. Allal, M. Fellah, M. R. Oudih et al, Eur. Phys. J. A, 27, s01:301-306 (2006)
[54]	N. Sandulescu, B. Erren and J. Dukelsky, Phys. Rev. C, 80:044335 (2009)
[55]	M. Fellah, N. H. Allal, Faiza Hammache et al, Int. J. Mod. Phys. E, 24:1550097 (2015)
[56]	K. Allaart and E. Boeker, Nucl. Phys. A, 168:630-662 (1971)
[57]	M. R. Oudih, M. Fellah and N. H. Allal, Int. J. Mod. Phys. E, 12:109-123 (2003)
[58]	M. V. Stoitsov, J. Dobaczewski, R. Kirchner, et al, Phys. Rev. C, 76:014308 (2007)
[59]	H. Olofsson, R. Bengtsson and P. Moller, Nucl. Phys. A, 784:104-146 (2007)
[60]	M. R. Oudih, M. Fellah, N. H. Allal et al, Phys. Rev. C, 76:047307 (2007)
[61]	A. A. Raduta, M. I. Krivoruchenko and A. Faessler, Phys. Rev. C, 85:054314 (2012)
[62]	A. A. Raduta and E. Moya de Guerra, Ann. Phys. (NY), 284:134-166 (2000)
[63]	K. Sieja, T. L. Ha, P. Quentin et al., Int. J. Mod. Phys. E, 16:289-298 (2007)
[64]	L. Bonneau, P. Quentin, and K. Sieja, Phys. Rev. C, 76:014304 (2007)
[65]	H. Laftchiev, J. Libert, P. Quentin et al, Nucl. Phys. A, 845:33-57 (2010)
[66]	K. W. Schmid, F. Grummer and A. Faessler, Ann. Rev. (NY), 180:1-73 (1987)
[67]	A. Petrovici, K. W. Schmid and Amand Faessler, Nucl. Phys. A, 647:197-216 (1999)
[68]	A. Petrovici, K. W. Schmid and Amand Faessler, Nucl. Phys. A, 728:396-414 (2003)
[69]	R. R. Chassman, Phys. Rev. Lett., 95:262501 (2005)
[70]	R. R. Chassman and P. Van Isacker, Phys. Lett. B, 685:55-58 (2010)
[71]	A. Mukherjee, Y. Alhassid, and G. F. Bertsch, Phys. Rev. C, 83:014319 (2011)
[72]	L.Y. Jia, Phys. Rev. C, 88:044303 (2013)
[73]	L. Y. Jia, Nucl. Phys. A, 941:293-306 (2015)
[74]	J. Q. Chen, Nucl. Phys. A, 626:686-714 (2000)
[75]	Y. M. Zhao, N. Yoshinaga, S. Yamaji et al, Phys. Rev. C, 62:014304 (2000)
[76]	G. J. Fu, Y. Lei, Y. M. Zhao et al, Phys. Rev. C, 87:044310 (2013)
[77]	S. Shlomo and I. Talmi, Nucl. Phys. A, 198:81-108 (1972)
[78]	L. Y. Jia, J. Phys. G:Nucl. Part. Phys., 42:115105 (2015)
[79]	M.-J. Cheng, L. Liu, and Y.-X. Zhang, Chin. Phys. C, 39:104102 (2015)
[80]	N. K. Timofeyuk, Phys. Rev. C, 81:064306 (2010)
[81]	O. Jensen, G. Hagen, T. Papenbrock et al, Phys. Rev. C, 82:014310 (2010)
[82]	F. Flavigny, Dtermination de facteurs spectroscopiques absolus par ractions de knockout et de transfert, Ph. D. Thesis (Universit Paris-Sud 6, 2011) (in French)
[83]	P. C. Srivastava and V. Kumar, Phys. Rev. C, 94:064306 (2016)
[84]	M. B. Tsang, Jenny Lee, and W. G. Lynch, Phys. Rev. Lett., 95:222501 (2005)
[85]	F. Beck, D. Frekers, P. von Neumann-Cosel et al, Phys. Lett. B, 645:128-132 (2007)
[86]	Jenny Lee, M. B. Tsang and W. G. Lynch, Phys. Rev. C, 75:064320 (2007)
[87]	M. B. Tsang, Jenny Lee, S. C. Su et al, Phys. Rev. Lett., 102:062501 (2009)
[88]	Sh. Hamada, N. Burtebayev, and N. Amangeldi, Int. J. Mod. Phys. E, 23:1450061 (2014)
[89]	N. Burtebayev, J. T. Burtebayeva, A. Duisebayev et al, Acta Phys. Pol. B, 46:1037-1054 (2015)
[90]	Vishal Srivastava, C. Bhattacharya, T. K. Rana et al, Phys. Rev. C, 93:044601 (2016)
[91]	F. Wang, B. H. Sun, Z. Liu et al, Phys. Lett. B, 770:83-87 (2017)
[92]	M. Horoi, J. Phys.:Conf. Ser., 413:012020 (2013)
[93]	P. O. Hess, A. Algora, J. Cseh et al, Phys. Rev. C, 70:051303 (R) (2004)
[94]	N. K. Timofeyuk, Phys. Rev. C, 88:044315 (2013)
[95]	H. T. Fortune and R. Sherr, Phys. Rev. C, 85:027305 (2012)
[96]	N. V. Gnezdilov, E. E. Saperstein, and S. V. Tolokonnikov, Phys. Atom. Nucl., 78:27-37 (2015)
[97]	E. Baranger and T. T. S. Kuo, Nucl. Phys. A, 97:289-297 (1967)
[98]	S. Aberg, P. B. Semmes and W. Nazarewicz, Phys. Rev. C, 56:1762-1773 (1997)
[99]	C. Basu, Pramana J. Phys., 63:1047-1052 (2004)
[100]	J. M. Yao, B. Sun, P. J. Woods et al, Phys. Rev. C, 77:024315 (2008)
[101]	H. F. Zhang, Y. J. Wang, J. M. Dong et al, J. Phys. G:Nucl. Part. Phys., 37:085107 (2010)
[102]	K. Kumar, J. B. Gupta, and J. H. Hamilton, Nucl. Phys. A, 448:36-44 (1986)
[103]	Y. Benbouzid, N. H. Allal, and M. Fellah, Rom. Journ. Phys., 61:424-434 (2016)
[104]	R. R. Chasman, Phys. Lett. B, 524:81-86 (2002)
[105]	R. W. Richardson, and N. Sherman, Nucl. Phys., 52:253-268 (1964)
[106]	R. D. Woods and D. S. Saxon, Phys. Rev., 95:577-578 (1954)
[107]	N. H. Allal and M. Fellah, Phys. Rev. C, 50:1404-1411 (1994)
[108]	S. Goriely, F. Tondeur, and J. M. Pearson, Atom. Data Nucl. Data Tables, 77:311-381 (2001)
[109]	P. Moller, J. R. Nix, W. D. Myers et al, Atom. Data Nucl. Data Tables, 59:185-381 (1995)
[110]	M. Wang, G. Audi, A. H. Wapstra et al, Chin. Phys. C, 36:1603 (2012)

[1]	B. S. Ishkhanov , S. V. Sidorov , T. Yu. Tretyakova , E. V. Vladimirova . Empirical pairing gaps and neutron-proton correlations. Chinese Physics C, 2019, 43(1): 014104. doi: 10.1088/1674-1137/43/1/014104
[2]	B. S. Ishkhanov;S. V. Sidorov;T. Yu. Tretyakova;E. V. Vladimirova . Empirical pairing gaps and neutron-proton correlations. Chinese Physics C, 2019, df87c41e-622f-49a7-b081-5c584df157aa(11): 14104-.
[3]	Zhi-Xing Zhang , Jian-Min Dong . A formula for half-life of proton radioactivity. Chinese Physics C, 2018, 42(1): 014104. doi: 10.1088/1674-1137/42/1/014104
[4]	Zhi-Hong Li , Er-Tao Li , Jun Su , Yun-Ju Li , You-Bao Wang , Sheng-Quan Yan , Bing Guo , Ding Nan , Wei-Ping Liu . New determination of the ⁷Be ground state spectroscopic factor and the ⁶Li(p,γ)⁷Be astrophysical S(E) factors. Chinese Physics C, 2018, 42(6): 065001. doi: 10.1088/1674-1137/42/6/065001
[5]	Benbouzid N , Allal M , Fellah M . Isovector pairing and particle-number fluctuation effects on the spectroscopic factors of one-proton stripping and one-neutronpick-up reactions in proton-rich nuclei. Chinese Physics C, 2018, 42(8): 084104. doi: 10.1088/1674-1137/42/8/084104
[6]	B. S. Ishkhanov , S. V. Sidorov , T. Yu. Tretyakova , E. V. Vladimirova . Mass differences and neutron pairing in Ca, Sn and Pb isotopes. Chinese Physics C, 2017, 41(9): 094101. doi: 10.1088/1674-1137/41/9/094101
[7]	Chao Wen , Yi-Ping Xu , Dan-Yang Pang , Yan-Lin Ye . Quenching of neutron spectroscopic factors of radioactive carbon isotopes with knockout reactions within a wide energy range. Chinese Physics C, 2017, 41(5): 054104. doi: 10.1088/1674-1137/41/5/054104
[8]	Zhen-Hua Zhang , Peng Xu . Investigation of the high-spin rotational properties of the proton emitter ¹¹³Cs using a particle-number conserving method. Chinese Physics C, 2017, 41(2): 024103. doi: 10.1088/1674-1137/41/2/024103
[9]	Wenjin Tan , Dongdong Ni , Zhongzhou Ren . Calculations of the β-decay half-lives of neutron-deficient nuclei. Chinese Physics C, 2017, 41(5): 054103. doi: 10.1088/1674-1137/41/5/054103
[10]	CHENG Ming-Jian , LIU Lang , ZHANG Yi-Xin . Particle-number fluctuation of pairing correlations for Dy isotopes. Chinese Physics C, 2015, 39(10): 104102. doi: 10.1088/1674-1137/39/10/104102
[11]	LIU Zhong-Jie , TANG Qi , ZHAN Xia-Yu , CHEN Jia-Bin , SONG Zi-Feng . Uncertainties induced by statistical fluctuations in fast mono-energetic neutron yield measurements. Chinese Physics C, 2014, 38(10): 106201. doi: 10.1088/1674-1137/38/10/106201
[12]	YANG Lin-Meng , GUO Wen-Jun , ZHANG Yun-Peng , ZHANG Xiao-Ji . Probing the symmetry potential with neutron-proton bremsstrahlung in heavy-ion collisions. Chinese Physics C, 2014, 38(7): 074105. doi: 10.1088/1674-1137/38/7/074105
[13]	LI Bing-Huan , ZHANG Zhen-Hua , LEI Yi-An . Particle-number conserving analysis for the 2-quasiparticle and high-K multi-quasiparticle states in doubly-odd ^174,176Lu. Chinese Physics C, 2013, 37(1): 014101. doi: 10.1088/1674-1137/37/1/014101
[14]	ZHU Xiang-Rong , ZHOU Dai-Cui . Gluon number fluctuations with heavy quarks at HERA. Chinese Physics C, 2011, 35(10): 902-907. doi: 10.1088/1674-1137/35/10/003
[15]	ZHANG Zhen-Hua , XU Hong-Qiao , SUN Bao-Xi . Particle-number conserving analysis of the high-K multi-quasiparticle bands in ¹⁷⁹Re. Chinese Physics C, 2010, 34(12): 1836-1841. doi: 10.1088/1674-1137/34/12/009
[16]	ZHENG Yong-Nan , ZHOU Dong-Mei . Nuclear structure of proton-rich unstable nucleus ²⁸P studied by g-factor measurement. Chinese Physics C, 2009, 33(S1): 215-217. doi: 10.1088/1674-1137/33/S1/069
[17]	FAN Ping , YUAN Da-Qing , ZUO Yi , ZHENG Yong-Nan , ZHOU Dong-Mei , WU Xiao-Guang , LI Guang-Sheng , ZHU Li-Hua , XU Guo-Ji , FAN Qi-Wen , ZHANG Xi-Zhen , ZHU Sheng-Yun . Proton alignment in ⁸²Sr investigated by g-factor measurements. Chinese Physics C, 2009, 33(S1): 206-208. doi: 10.1088/1674-1137/33/S1/066
[18]	M. Sudol (for \=PANDA collaboration) . Time-like proton form factor measurement with PANDA. Chinese Physics C, 2009, 33(12): 1244-1248. doi: 10.1088/1674-1137/33/12/031
[19]	Jin Taihao , Zhao Zhengji , Zeng Jinyan . Particle-Number Conserving Calculation of the Bandhead Moments of Inertia of Identical SD Bands. Chinese Physics C, 1993, 17(S4): 411-421.
[20]	Cheng Tansheng , Wu Chongshi , Zeng Jinyan . Particle-Number-Conserving Approach for Treating Cranking Hamiltonian. Chinese Physics C, 1988, 12(S3): 313-320.

Access

Get Citation

Y. Benbouzid, N. H. Allal, M. Fellah and M. R. Oudih. Influence of isovector pairing and particle-number projection effects on spectroscopic factors for one-pair like-particle transfer reactions in proton-rich even-even nuclei[J]. Chinese Physics C, 2018, 42(4): 044103. doi: 10.1088/1674-1137/42/4/044103

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2018-01-15

Article Metric

Article Views(1537)
PDF Downloads(30)
Cited by(0)

Policy on re-use

To reuse of subscription content published by CPC, the users need to request permission from CPC, unless the content was published under an Open Access license which automatically permits that type of reuse.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Influence of isovector pairing and particle-number projection effects on spectroscopic factors for one-pair like-particle transfer reactions in proton-rich even-even nuclei

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article

Influence of isovector pairing and particle-number projection effects on spectroscopic factors for one-pair like-particle transfer reactions in proton-rich even-even nuclei

HTML

目录