Neutron-proton pair correlation from a shell-model perspective$

Transcription

1 L"B#!"-A)"'*%"'&#:%)>5.%M#%N#OAI-)%"P EDR6#S#P#T#/I&;#LUVW#!"#$%&'()$*+,"*"-".$ &/$".0#+&)&1'$ Neutron-proton pair correlation from a shell-model perspective$ Chong Qi KTH Royal institute of Technology, Stockholm "#$%&&'(%)'*%"#+,-.#/0#1&%234,5-6#70#8,%9'6#70#:;556#<0#1=$>6#?0#/%."5%"6#10#@ABA)+'&&#CD<EF# "B#G0#HI#C1A,J,"KF#

2 The coupling of few nucleons!! Seniority and systems with identical particles in single-j and many-j orbitals Pairing gap and pair correlation!! Neutron-proton correlation from the binding energy The residual np interaction/energy!! Neutron-proton spin-aligned pair coupling "J=1 pair "Quartet 2$$$$$$$$$3$$$ JJ#$%IM&,"K#,5#N'4%)AB#,"#"I$&A')#5;5-A2 "4566$7869:;<=$><5:;=6?$ X"A#$'"#)A2%4A#'#/YZU#M',)#,"#)A'$*%"5#

3 16965<=$>5F>65:6?$FG$H46$6I6;:J6$79H65<;:F9$!!!5%4A$-%)#C<ZVF[#/ZU6L6006L/PV6#/ZU#-A)2#'9)'$*4A#!"#$%$&'()*%-.A)5#$&%5A#-%#\A)%#!!!5%5$'&')#C<ZUF[#/ZV6]6006LJ6#5-)%"K&;#'9)'$*4A#C2A'"#^A&BF# #!+,-*./0*#&1*23*4-%56*#%-*4,-*5764*#8%#9:;-*7&-6<* #!+,-*#B$'&-1*"#$%6*A7%*1$C-%-&4*3*6,-BB6*,#;-*1$C-%-&4*#&'DB#%*575-&4D5* #!57%-*1-4#$B6*'$;-&*$&*E#&#1#FG&HI7*#&1**J#99,$#;-BB$K6*4#BL6<* "! = 0 "! = 0 2+ "! = ! J jn B@C$ B@DE$ B@A$ cos"12 = J(J +1) #1 2 j( j +1).<M<*N9,$C-%*#&1*O<O<*+%D-)*P-;<J71<M,I6<*QR)0S0*!0STU(*

4 O4<H$7?$H46$PN797N<=P$NF86=$F96$9668?Q$ ($:9K$><5H$FG$H46$R<J6$GL9;:F9$N<K$;<55K$H46$NF?H$7N>F5H<9H$79GF5N<:F9,697F57HK$;FL>=79M$GF5$N<9K$?46==?$ $ # 10 2 in seniority space Easier to include many shells!! X"A#$'"#)A'B,&;#5%&4A#'#.'&NP^&&AB#5;5-A2#+,-.#IM-%#]SP]_#B%I(&;P# BAKA"A)'-A#%)(,-'&5#'"B#V_PVT#M',)5#C`,2[#TaVU T P]0WaVU VU 6#5.A&&P 2%BA&#B,2A"5,%"[#baVU LU PcaVU LV F0#!! R"&,>A#1@d6#-.A#M',)5#B%#"%-#"A$A55'),&;#.'4A#-.A#5'2A#5-)I$-I)A#

5 Seniority coupling and binding energy Semi-magic nuclei Binding energies of ground states in j n configuration ( ) = Cn n(n 1)α + $ 1 2 n E j n " # % & ' β Neutron separa*on energies from Ca isotopes Proton separa*on energies from N=28 isotones I. Talmi, Simple models of complex nuclei (Harwood, Chur, Switzerland, 1993)

6 Seniority coupling and binding energy odd-even staggering

7 Equally- space doubly degenerate system (picket fence model) The total energy can be well approximated by a closed form BCS- like picture S.A. Changizi, C. Qi, R. Wyss, Nucl. Phys. A 940, 210 (2015)

8 Pairing gap and the alpha formation No Pairing A.N. Andreyev CQ et al., PhysRevLett (2013). Strong pairing

9 F??7U=6$N<97G6?H<:F9$79$FH465$FU?65J<U=6?$$ 5F??$?6;:F9?$FG$V>ZHX$56<;:F9?$F9$YU$7?FHF>6?$ M. Takahashi, PRC27,1454(1983)

10 Neutron-proton pairing correlation

11 "57J7<=$6[<N>=6?\$ "46$?>79$H5<>$7?FN65?\ The 12 + spin trap in 52 Fe WX)*M,I6<*P-;<*W*R0)*>YQY0R*!2>0>(<* The predicted 16 + spin trap in 96 Cd WX)*M,I6<*P-;<*W*R0)*>YQY0R*!2>0>(<* The relative positions of these spin traps are sensitive to the strength of the interaction V J=2j

12 The energy expression Number of pairs/interactions C J I = 1 2 " ( a + a + ) J a a # $ ( ) J 0 % &' #!For systems with n=4 and isospin T=0, there are three isoscalar pairs and three isovecto pairs; #!For those with T=2 (four identical nucleons), we have six isovector pairs. #!For 12 C assuming 8 valence nucleons, one has 10 T=0 pairs and 18 T=1 pairs G<*J7I#*1-*ZD-%%#)*[<*[<*P#1D4#)*=<*\#5$9L)*#&1*M<*N#%%$'D%-&)*VD9B<*M,I6<*[*!"!#$%$&"''%()$ WX)*M,I6<*P-;<*W**+#$'%,%+*$&"'+'()$ ]<*+#B5$)*VD9B<*M,I6<*[*RQU*!2>0>(*Y0<* g h

13 Seniority with isospin Odd-even staggering Pairing energy in mass formula

14 The average proton- neutron interac:on J.- Y. Zhang, R.F. Casten, D.S. Brenner, Phys. Le9. B 227 (1989) 1. CQ, Physics Letters B 717, 436 (2012)

15 Addi:onal binding for N=Z nuclei CQ, Physics Letters B 717, 436 (2012)

16 The residual np interac:on from binding energy

17 But many N=Z nuclei are deformed and favors the Nilsson picture N. Mărginean et al., PRC 63, (R) (2001) u QQ correla*on induces deforma*on; u The np interac*on also breaks the seniority in a major way

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19 _`08$VD9TD>X\$$($?7N>=6$6[<N>=6$HF$?4FR$H46$><75$;F9H69H$ R5I'&&;#-.A#+'4A#NI"$*%"#$'"#(A# AfM'"BAB#'5# <.A#-.I5#%(-',"AB#+'4A#NI"$*%"#,5#'#2,f-I)A#%N# 2'";#$%2M%"A"-#'5#'#)A5I&-#%N#-.A#"M#,"-A)'$*%"# <.A#5-),>,"K#NA'-I)A#,5#-.'-#,N#+A#M)%JA$-#,-#%"#-%#"M#$%IM&AB#-A)256#-.A#+'4A#NI"$*%"#$'"#(A# )AM)A5A"-AB#(;#'#5,"K&A#-A)2###

20 _`08$VD9TD>X\$$($?7N>=6$6[<N>=6$HF$?4FR$H46$><75$;F9H69H$ "46$;<=;L=<H68$?>6;H5LN$?4FR$<$6SL787?H<9H$><a659$ ($9<7J6$>7;HL56$7?$H4<H$H46$<9ML=<5$NFN69H<$FG$H46$?H<H6?$<56$M6965<H68$UK$H46$56<55<9M6N69H$FG$H46$ <9ML=<5$NFN69HLN$J6;HF5?$FG$H46$<=7M968$9>$><75?c$ $ $ _`08$ B@_$ *$ B@_$ 8 3 +

21 (J65<M6$9LNU65$FG$><75?$ I C J =0 I (nn) = C J =0 I (pp) = C J =0

22

23 Probe the pair content of the wave func*on by one- par*cle removal reac*ons?

24 "46$56=<:J6$NF:F9$FG$H46$9>$><75?$ _`08$ _D Y8$ <.A#-)'"5,*%"#5-)A"K-.5#)A2',"#'MM)%f,2'-A&;#-.A#5'2A#'&%"K#-.A#;)'5-#&,"A# <.A#1ClLF#4'&IA5#$%""A$*"K#;)'5-#5-'-A5#,"# TL QB#')A#-+%#*2A5#&')KA)#-.'"#-.%5A#%N#

25 "46$?>79T<=7M968$><75$>=<K?$<$;5L;7<=$-./0123$5F=6$!-#,5#5-)%"K&;#'9)'$*4A#5,"$A#-.,5#2'f,2'&&;#'&,K"AB#$%"^KI)'*%"#.'5#2'f,2'&#%4A)&'M#(A-+AA"# -.A#M)%-%"#'"B#"AI-)%"#+'4A#NI"$*%"5# da",%),-;p&,>a# l3i,b,5-'"-#m'9a)"#

26 _D Y8$ $&*" 0c2 *' Sc2 *6"#9-* <+%#M')*$&A#$%Aq$,A"-5#%N#N)'$*%"'&#M')A"-'KA# {[( j 2 ) J1 ( j 2 ) J 2 ] J 3 ( j 2 ) J 4 } J 5 ( j 2 ) J 6 G0H0#HI6#@0#e,6#/0#1&%234,5-6#70/0#8,%9'6#70#:;55#OI$&0#Q.;50#?#_cc6#WV#CLUVLF0

27 Non- unique ways to define a many- pair state CQ et al, PRC 84, (R) (2011). Z.X. Xu, C. Qi, J. Blomqvist, R.J. Lio9a, R. Wyss Nucl. Phys. A 877, 51 (2012). C. Qi, Prog. Theor. Suppl. 196, 414 (2012).

28 Quartefng Non- unique ways to define a many- pair state Z.X. Xu, C. Qi, J. Blomqvist, R.J. Lio9a, R. Wyss Nucl. Phys. A 877, 51 (2012). C. Qi, Prog. Theor. Suppl. 196, 414 (2012).

29 Quartefng Non- unique ways to define a many- pair state Z.X. Xu, C. Qi, J. Blomqvist, R.J. Lio9a, R. Wyss Nucl. Phys. A 877, 51 (2012). C. Qi, Prog. Theor. Suppl. 196, 414 (2012).

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32 The deformed f 7/2 nuclei N=Z even- even nuclei in single- j shells like 0f7/2, 0g9/2 and 0h11/2 show a vibra:onal like structure with func:ons virtually can be represented by the spin- aligned np coupling scheme.

33 #<N7=HF97<9$ D9TD>$V ii "7X$FLH?786$ ia 0<$ 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 NM#5.A&&# N# NcrL# BAKA"A)'-A#NcrL#'"B#NWrL#

34 Superallowed alpha decay around N=Z nuclei Shell model calcula*ons on the alpha forma*on amplitude in N=Z nuclei.

35 Summary Systems with iden*cal par*cles and the T=1 pairing The np pair correla*on from the binding energy difference Neutron- proton spin- aligned pair coupling in N=Z nuclei v Crucial building blocks of the nuclear many- body wave func:on. v Important part of the effec:ve two- body interac:on. v Exhibi:ng regular low- lying spectra and E2 transi:on probabili:es. Ongoing: v Extension to systems with many shells No available simple (one term) generator for the spectrum No available generator for mul:- j aligned pair v The response to deforma*on effects Averaged number of par:cles in different shells for 92 Pd

36 Thank you! 多謝

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