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Analysis of shape evolution for Pt isotopes with relativistic mean field theory

Wang Gang Fang Xiang-Zheng Guo Jian-You

Analysis of shape evolution for Pt isotopes with relativistic mean field theory

Wang Gang, Fang Xiang-Zheng, Guo Jian-You
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  • The relativistic mean field theory is used to investigate the shape evolution of Pt isotopes. The calculated binding energy and deformation parameter 2 are consistent with those obtained in experiment. The potential energy surfaces and the single particle levels show the shape evolution for Pt isotopes. From N=88 to N=126, the shapes for Pt nuclei evolve from spherical shapes to X(5), and then to shapes of stable quadruple deformation, finally back to the spherical shapes. In detail, 166-172Pt are spherical. 174Pt and 192-196Pt possess the X(5) symmetry. 176-190Pt are deformed nuclei. 204Pt holds spherical shape. These results in agreement with the experimental observations.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11175001), the Program for New Century Excellent Talents in University of China (Grant No. NCET-05-0558), the Program for Excellent Talents in Anhui Province, China (Grant No. 2007Z018), the Natural Science Foundation of Anhui Province, China (Grant No. 11040606M07), the Education Committee Foundation of Anhui Province, China (Grant No. KJ2009A129), and the 211 Project of Anhui University, China.
    [1]

    Vojta M, Zhang Y, Sachdev S 2000 Phys. Rev. Lett. 85 4940

    [2]

    Han S, Kuang-Tsan W, Kim R 2008 Opt. Express 16 873

    [3]

    Iachello F 2001 Phys. Rev. Lett. 87 052502

    [4]

    Casten R F, Zamfir N V 2001 Phys. Rev. Lett. 87 052503

    [5]

    Kruken R, Albanna B, Bialik C, Casten R F, Cooper J R, Dewald A, Zamfir N V, Barton C J, Beausang C W, Caprio M A, Hecht A A, Klug T, Novak J R, Pietralla N, Brentano P 2002 Phys. Rev. Lett. 88 232501

    [6]

    Tonev D, Dewald A, Klug T, Petkov P, Jolie J, Fitzler A, Möller O, Heinze S, Brentano P, Casten R F 2004 Phys. Rev. C 69 034334

    [7]

    Iachello F 2000 Phys. Rev. Lett. 85 3580

    [8]

    Casten R F, Zamfir N V 2000 Phys. Rev. Lett. 85 17

    [9]

    Frank A, Alonso C E, Arias J M 2001 Phys. Rev. C 65 014301

    [10]

    Zamfir N V, Caprio M A, Casten R F, Barton C J, Beausang C W, Berant Z, Brenner D S, Chou W T, Cooper J R, Hecht A A, Krucken R, Newman H, Novak J R, Pieralla N, Wolf A, Zyromski K E 2002 Phys. Rev. C 65 044325

    [11]

    Clark R M, Cromaz M, Deleplanque M A, Descovich M, Diamond R M, Fallon P, Lee I Y, Macchiavelli A O, Mahmud H, Rodriguez-Vieitez E, Stephens F S, Ward D 2004 Phys. Rev. C 69 064322

    [12]

    Mihai C, Zamfir N V, Bucurescu D, Cata-Danil G, Cata-Danil I, Ghita D G, Ivascu M, Sava T, Stroe L, Suliman G 2007 Phys. Rev. C 75 044302

    [13]

    Kondev F G, Carpenter M P, Janssens R V F, Wiedenhover I, Alcorta M, Brown L T, Davids C N, Khoo T L, Lauritsen T, Lister C J, Seweryniak D, Siem S, Sonzogni A A, Uusitalo J 2000 Phys. Rev. C 61 044323

    [14]

    Blanc F L, Lunney D, Obert J, Oms J, Putaux J C, Roussiere B, Sauvage J, Zemlyanoi S, Pinard J, Cabaret L, Duong H T, Huber G, Krieg M, Sebastian V, Crawford J E, Lee J K P, Girod M, Péru S, Genevey J, Lettry J 1999 Phys. Rev. C 60 054310

    [15]

    Joss D T, Simpson J, Appelbe D E, Barton C J, Warner D D, Lagergren K, Cederwall B, Hadinia B, Eeckhaudt S, Grahn T, Greenlees P T, Jones P M, Julin R, Juurinen S, Kettunen H, Leino M, Leppanen A P, Nieminen P, Pakarinen J, Perkowski J, Rahkila P, Scholey C, Uusitalo J, van de Vel K, Page R D, Paul E S, Wiseman D R, Riley M A 2006 Phys. Rev. C 74 014302

    [16]

    Popescu D G, Waddington J C, Cameron J A, Johansson J K, Schmeing N C, Schmitz W, Carpenter M P, Janzen V P, Nyberg J, Riedinger L L, Hubel H, Kajrys G, Monaro S, Pilotte S, Bourgeois C, Perrin N, Sergolle H, Hojman D, Korichi A 1997 Phys. Rev. C 55 1175

    [17]

    Xu Y, Krane K S, Gummin M A, Jarrio M, Wood J L, Carter H K 1992 Phys. Rev. Lett. 68 3853

    [18]

    Sauvage-Letessier J, Quentin P, Flocard H 1981 Nucl. Phys. A 370 231

    [19]

    Ansari A 1986 Phys. Rev. C 33 321

    [20]

    Bonche P, Krieger S J, Quentin P, Weiss M S, Meyer J, Meyer M, Redon N, Flocard H, Heenen P H 1989 Nucl. Phys. A 500 308

    [21]

    Bengtsson R, Bengtsson T, Dudek J, Leander G, Nazarewicz W, Zhang J Y 1987 Phys. Rev. Lett. B 183 1

    [22]

    Möller P, Nix J R, Myers W D, Swiatecki W J 1995 At. Data Nucl. Data Tables 59 185

    [23]

    Möller P, Bengtsson R, Carlsson B G, Olivius P, Ichikawa T, Sagawa H, Lwamoto A 2008 At. Data Nucl. Data Tables 94 758

    [24]

    Audi G, Wapstra A H, Thibault C 2003 Nucl. Phys. A 729 337

    [25]

    Hilberath T, Becker S, Bollen G, Kluge H J, Kronert U, Passler G, Rikovska J, Wyss R, Collaboration I 1992 Z. Phys. A 342 1

    [26]

    Fossion R, Bonatsos D, Lalazissis G A 2006 Phys. Rev. C 73 044310

    [27]

    Furnstahl R J 2002 Nucl. Phys. A 706 85

    [28]

    Meng J, Ring P 1996 Phys. Rev. Lett. 77 3963

    [29]

    Meng J, Ring P 1998 Phys. Rev. Lett. 80 460

    [30]

    Meng J, Zhang W, Zhou S G, Toki H, Geng L S 2005 Eur. Phys. J. A 25 23

    [31]

    Sheng Z Q, Guo J Y 2005 Mod. Phys. Lett. A 35 2711

    [32]

    Niksić T, Vretenar D, Lalazissis G A, Ring P 2007 Phys. Rev. Lett. 99 092502

    [33]

    Niksić T, Li Z P, Vretenar D, Próchniak L, Meng J, Ring P 2009 Phys. Rev. C 79 034303

    [34]

    Li Z P, Niksić T, Vretenar D, Meng J, Lalazissis G A, Ring P 2009 Phys. Rev. C 79 054301

    [35]

    Li Z P, Niksić T, Vretenar D, Meng J 2009 Phys. Rev. C 80 061301

    [36]

    Li Z P, Niksić T, Vretenar D, Meng J 2010 Phys. Rev. C 81 034316

    [37]

    Guo J Y, Jiao P, Fang X Z 2010 Phys. Rev. C 82 047301

    [38]

    Zhang W, Li Z P, Zhang S Q, Meng J 2010 Phys. Rev. C 81 034302

    [39]

    Ren Z Z, Faeaaler A, Bohyk A 1998 Phys. Rev. C 57 2752

    [40]

    Serot B D, Walecka J D 1986 Nucl. Phys. A 16 1

    [41]

    Chen D H, Tai F, Ren Z Z 2003 High Energy Phys. Nucl. Phys. 27 707 (in Chinese) [陈鼎汉, 邰非, 任中洲 2003 高能物理与核物理 27 707]

    [42]

    Ring P 1996 Prog. Part. Nucl. Phys. 37 193

    [43]

    Camhhir Y K, Ring P, Thimet A 1990 Ann. Phys. (N.Y.) 198 132

    [44]

    Ren Z Z, Toki H 2001 Nucl. Phys. A 689 691

    [45]

    Long W H, Meng J, Giai N V, Zhou S G 2004 Phys. Rev. C 69 034319

    [46]

    Lalazissis G A, König J, Ring P 1997 Phys. Rev. C 55 1

    [47]

    Sharma M M, Ring P 1991 Phys. Rev. C 45 5

    [48]

    Sugahara Y, Toki H 1994 Nucl. Phys. A 579 557

    [49]

    Raman S, Nestor Jr. C W, Tikkanen P 2001 At. Data Nucl. Data Tables 78 1

  • [1]

    Vojta M, Zhang Y, Sachdev S 2000 Phys. Rev. Lett. 85 4940

    [2]

    Han S, Kuang-Tsan W, Kim R 2008 Opt. Express 16 873

    [3]

    Iachello F 2001 Phys. Rev. Lett. 87 052502

    [4]

    Casten R F, Zamfir N V 2001 Phys. Rev. Lett. 87 052503

    [5]

    Kruken R, Albanna B, Bialik C, Casten R F, Cooper J R, Dewald A, Zamfir N V, Barton C J, Beausang C W, Caprio M A, Hecht A A, Klug T, Novak J R, Pietralla N, Brentano P 2002 Phys. Rev. Lett. 88 232501

    [6]

    Tonev D, Dewald A, Klug T, Petkov P, Jolie J, Fitzler A, Möller O, Heinze S, Brentano P, Casten R F 2004 Phys. Rev. C 69 034334

    [7]

    Iachello F 2000 Phys. Rev. Lett. 85 3580

    [8]

    Casten R F, Zamfir N V 2000 Phys. Rev. Lett. 85 17

    [9]

    Frank A, Alonso C E, Arias J M 2001 Phys. Rev. C 65 014301

    [10]

    Zamfir N V, Caprio M A, Casten R F, Barton C J, Beausang C W, Berant Z, Brenner D S, Chou W T, Cooper J R, Hecht A A, Krucken R, Newman H, Novak J R, Pieralla N, Wolf A, Zyromski K E 2002 Phys. Rev. C 65 044325

    [11]

    Clark R M, Cromaz M, Deleplanque M A, Descovich M, Diamond R M, Fallon P, Lee I Y, Macchiavelli A O, Mahmud H, Rodriguez-Vieitez E, Stephens F S, Ward D 2004 Phys. Rev. C 69 064322

    [12]

    Mihai C, Zamfir N V, Bucurescu D, Cata-Danil G, Cata-Danil I, Ghita D G, Ivascu M, Sava T, Stroe L, Suliman G 2007 Phys. Rev. C 75 044302

    [13]

    Kondev F G, Carpenter M P, Janssens R V F, Wiedenhover I, Alcorta M, Brown L T, Davids C N, Khoo T L, Lauritsen T, Lister C J, Seweryniak D, Siem S, Sonzogni A A, Uusitalo J 2000 Phys. Rev. C 61 044323

    [14]

    Blanc F L, Lunney D, Obert J, Oms J, Putaux J C, Roussiere B, Sauvage J, Zemlyanoi S, Pinard J, Cabaret L, Duong H T, Huber G, Krieg M, Sebastian V, Crawford J E, Lee J K P, Girod M, Péru S, Genevey J, Lettry J 1999 Phys. Rev. C 60 054310

    [15]

    Joss D T, Simpson J, Appelbe D E, Barton C J, Warner D D, Lagergren K, Cederwall B, Hadinia B, Eeckhaudt S, Grahn T, Greenlees P T, Jones P M, Julin R, Juurinen S, Kettunen H, Leino M, Leppanen A P, Nieminen P, Pakarinen J, Perkowski J, Rahkila P, Scholey C, Uusitalo J, van de Vel K, Page R D, Paul E S, Wiseman D R, Riley M A 2006 Phys. Rev. C 74 014302

    [16]

    Popescu D G, Waddington J C, Cameron J A, Johansson J K, Schmeing N C, Schmitz W, Carpenter M P, Janzen V P, Nyberg J, Riedinger L L, Hubel H, Kajrys G, Monaro S, Pilotte S, Bourgeois C, Perrin N, Sergolle H, Hojman D, Korichi A 1997 Phys. Rev. C 55 1175

    [17]

    Xu Y, Krane K S, Gummin M A, Jarrio M, Wood J L, Carter H K 1992 Phys. Rev. Lett. 68 3853

    [18]

    Sauvage-Letessier J, Quentin P, Flocard H 1981 Nucl. Phys. A 370 231

    [19]

    Ansari A 1986 Phys. Rev. C 33 321

    [20]

    Bonche P, Krieger S J, Quentin P, Weiss M S, Meyer J, Meyer M, Redon N, Flocard H, Heenen P H 1989 Nucl. Phys. A 500 308

    [21]

    Bengtsson R, Bengtsson T, Dudek J, Leander G, Nazarewicz W, Zhang J Y 1987 Phys. Rev. Lett. B 183 1

    [22]

    Möller P, Nix J R, Myers W D, Swiatecki W J 1995 At. Data Nucl. Data Tables 59 185

    [23]

    Möller P, Bengtsson R, Carlsson B G, Olivius P, Ichikawa T, Sagawa H, Lwamoto A 2008 At. Data Nucl. Data Tables 94 758

    [24]

    Audi G, Wapstra A H, Thibault C 2003 Nucl. Phys. A 729 337

    [25]

    Hilberath T, Becker S, Bollen G, Kluge H J, Kronert U, Passler G, Rikovska J, Wyss R, Collaboration I 1992 Z. Phys. A 342 1

    [26]

    Fossion R, Bonatsos D, Lalazissis G A 2006 Phys. Rev. C 73 044310

    [27]

    Furnstahl R J 2002 Nucl. Phys. A 706 85

    [28]

    Meng J, Ring P 1996 Phys. Rev. Lett. 77 3963

    [29]

    Meng J, Ring P 1998 Phys. Rev. Lett. 80 460

    [30]

    Meng J, Zhang W, Zhou S G, Toki H, Geng L S 2005 Eur. Phys. J. A 25 23

    [31]

    Sheng Z Q, Guo J Y 2005 Mod. Phys. Lett. A 35 2711

    [32]

    Niksić T, Vretenar D, Lalazissis G A, Ring P 2007 Phys. Rev. Lett. 99 092502

    [33]

    Niksić T, Li Z P, Vretenar D, Próchniak L, Meng J, Ring P 2009 Phys. Rev. C 79 034303

    [34]

    Li Z P, Niksić T, Vretenar D, Meng J, Lalazissis G A, Ring P 2009 Phys. Rev. C 79 054301

    [35]

    Li Z P, Niksić T, Vretenar D, Meng J 2009 Phys. Rev. C 80 061301

    [36]

    Li Z P, Niksić T, Vretenar D, Meng J 2010 Phys. Rev. C 81 034316

    [37]

    Guo J Y, Jiao P, Fang X Z 2010 Phys. Rev. C 82 047301

    [38]

    Zhang W, Li Z P, Zhang S Q, Meng J 2010 Phys. Rev. C 81 034302

    [39]

    Ren Z Z, Faeaaler A, Bohyk A 1998 Phys. Rev. C 57 2752

    [40]

    Serot B D, Walecka J D 1986 Nucl. Phys. A 16 1

    [41]

    Chen D H, Tai F, Ren Z Z 2003 High Energy Phys. Nucl. Phys. 27 707 (in Chinese) [陈鼎汉, 邰非, 任中洲 2003 高能物理与核物理 27 707]

    [42]

    Ring P 1996 Prog. Part. Nucl. Phys. 37 193

    [43]

    Camhhir Y K, Ring P, Thimet A 1990 Ann. Phys. (N.Y.) 198 132

    [44]

    Ren Z Z, Toki H 2001 Nucl. Phys. A 689 691

    [45]

    Long W H, Meng J, Giai N V, Zhou S G 2004 Phys. Rev. C 69 034319

    [46]

    Lalazissis G A, König J, Ring P 1997 Phys. Rev. C 55 1

    [47]

    Sharma M M, Ring P 1991 Phys. Rev. C 45 5

    [48]

    Sugahara Y, Toki H 1994 Nucl. Phys. A 579 557

    [49]

    Raman S, Nestor Jr. C W, Tikkanen P 2001 At. Data Nucl. Data Tables 78 1

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  • Received Date:  29 June 2011
  • Accepted Date:  28 May 2012
  • Published Online:  05 May 2012

Analysis of shape evolution for Pt isotopes with relativistic mean field theory

  • 1. School of Physics and Material Science, Anhui University, Hefei 230039, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11175001), the Program for New Century Excellent Talents in University of China (Grant No. NCET-05-0558), the Program for Excellent Talents in Anhui Province, China (Grant No. 2007Z018), the Natural Science Foundation of Anhui Province, China (Grant No. 11040606M07), the Education Committee Foundation of Anhui Province, China (Grant No. KJ2009A129), and the 211 Project of Anhui University, China.

Abstract: The relativistic mean field theory is used to investigate the shape evolution of Pt isotopes. The calculated binding energy and deformation parameter 2 are consistent with those obtained in experiment. The potential energy surfaces and the single particle levels show the shape evolution for Pt isotopes. From N=88 to N=126, the shapes for Pt nuclei evolve from spherical shapes to X(5), and then to shapes of stable quadruple deformation, finally back to the spherical shapes. In detail, 166-172Pt are spherical. 174Pt and 192-196Pt possess the X(5) symmetry. 176-190Pt are deformed nuclei. 204Pt holds spherical shape. These results in agreement with the experimental observations.

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