МУЛЬТИПОЛЬНЫЕ РЕЗОНАНСЫ ФОТО- И...
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МУЛЬТИПОЛЬНЫЕ РЕЗОНАНСЫ
ФОТО- И ЭЛЕКТРОВОЗБУЖДЕНИЯ ЯДЕР
SD- ОБОЛОЧКИ
Н.Г.Гончарова
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Particle Core Coupling (PCC) version of the Shell Model
•'
'
(J ), ji, i i
(J ), jA 1 i iJ T C (J 'E'T') (nlj) : J ,T−= ×∑
'
' '
(J ), j'f , f f
(J ), jA 1 f fJ T (J 'E'T') (n 'l' j') : J ,T−= ×∑α
ii
i
SCS
≈∑
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Matrix elements of Hamiltonian
ij j c ij ijH (E ' E ) V= + + +ε δ
ijV =
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Nuclear photo- and electroexcitations
( ) ( ) ( )4 2
2 2 2ML T4 2
R
q qd e,e 4 F q, tg F q,d q 2q 2
μ μ⎧ ⎫⎛ ⎞ ⎛ ⎞′σ πσ θ⎪ ⎪= ω + + ω⎜ ⎟ ⎜ ⎟⎨ ⎬⎜ ⎟ ⎜ ⎟Ω η ⎪ ⎪⎝ ⎠ ⎝ ⎠⎩ ⎭
( ) ( ) { } ( )max maxJ J2 212 el mag 2 2
T i f J i f J i EJ MJJ 1 J 1
F q 2J 1 J T (q) J J T (q) J F F−
= =
= + + = +∑ ∑
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Summed squared form factors: electroexcitation of sd-shell nuclei
1ħω resonances in sd-shell nuclei: E1, M2, E3, M4, E5, M6
Photopoint : 1
excq E 0.1 0.2Fmω −= ≡ ≈ ÷
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Spectroscopy of pickup reactions on 18O
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E1 in 18O at photopoint
2/52/3
2/32/3
2/12/3
111121
dpdpsp
→→→
2/52/5
2/32/5
2/72/5
112111
fdpdfd
→→→
U.Kneissl ea // Nucl.Phys.A272,125 (1976)
18O(γ,n)
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Spectroscopy of pickup reactions on 22Ne
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E1 in 22Ne at photopoint
22Ne(γ,n)V.V.Varlamov,M.E.StepanovMSU-INP,1999
ii
i
SCS
≈∑
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E1 in 24Mg at photopoint
15.00 20.00 25.00 30.00 35.000.00
0.10
0.20
0.30
0.40 a
15.00 20.00 25.00 30.00 35.000.0
10.0
20.0
30.0 b
F2 × 102
σ, mb
Exp: Ishkhanov B.S. ea., Nucl. Phys.A186 (1972) 438
P.M. Endt, Nucl.Phys.A521(1990)1
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E1 in 26Mg at photopointF2 × 102
Exp (c): (γ, n)+(γ, n+p)+(γ, 2n) Fultz S.C. et al., Phys. Rev. C4 (1971) 149
σ, mb
E, MeV
10.00 20.00 30.00 40.000.00
0.40
0.80a
10.00 20.00 30.00 40.000.0
20.0
40.0c
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27Al+γ → 26Al+n
Exp: M.N.Thompson et al // Nucl. Phys. 64 (1965)486
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Динамические деформации при фоторасщеплении 27Al
• 27Al+γ → 26Al+n 27Al+γ → 26Mg+p
H. Röpke, P.M.Endt // Nucl. Phys. A632(1998)173.
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Спектроскопия реакции подхвата32S(d,3He)31P
Спектроскопия реакции 32S(d,3He)31P;Е*- энергии возбуждения ядра 31P
J.Vernotte et al,Nucl.Phys.A655(1999)415
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E1 excitations 32S
Exp: B.S.ISHKHANOV et al,2002.PCC version of SM
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Спектроскопия реакции подхвата34S(p,d)33S
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34S – photoneutron reaction
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E1 excitation of 48Ca
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Excitation and disintegration of 48Ca(isospin factors)
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48Ca( , n)γ
O’Keefe G.J. , Thompson M.N. et al // Nucl.Phys.A469(1987) 239
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48Ca( ,p)γ
O’Keefe G.J. , Thompson M.N. et al // Nucl.Phys.A469(1987) 239
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E1 resonances in (e.e’)Spin- and orbital currents interference in E1 sd-shell form factors
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For E1 transitions
maxima of C1 form factors (a) are near minima of E1 form factors(b)
1/2 3/21 1( 1)= + = +⇒ +j L j LL L
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F2(q) for E1 transitions
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MJmax excitations
max
2 222 2( ) exp( )
2∼ J
MJ f J ib q
F J O q J C q= × −
max2J
qb
=
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MJmax (stretched states)
Spin current contributions only
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M6 in sd-shell nuclei : 28Si
E, MeV
q = 1.8 Fm-1
S.Yen,ea,Phys.Lett.B289, 22(1992):6- T=1 at 14.32 MeV
Endt P.M. Nucl. Phys. A 310 (1978)
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M6 in sd-shell nuclei : 32S
Exp.: Clausen B.L et al , Phys.Rev.C48, 1632(1993).
Exp
q = 1.8 Fm-1
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M6 in Ca-40
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M2 resonances
Spin- an orbital currents in M2 excitations
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Nuclear Orbital M2 CurrentOrbital M2 TWIST Mode: Orbital current has oppositesignes in the upper and lower semispheres.The current vanishes at
Z=0
( ) ( )( )2
2 2 22 =
⎡ ⎤Υ Ω ×∇⎣ ⎦∼Jmag i
j i jeT j qrq
(e,e’) excitation ~Spin+orbital(twist)
modes
(p,p’) excitations –SPIN part onlyComparison of (e,e’) and (p,p’) reveals
ORBITAL TWIST M2-
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M2 in 32S(e,e’)
Experiment: S-DALINAC (Emax=14 MeV) E, MeV
F2 × 105
8.00 12.00 16.00 20.000.000.501.001.502.002.50
S-320.7 g free
8.00 12.00 16.00 20.000.0
4.0
8.0
12.0
16.0S-32
F2 × 106
q = 0.6 fm-1
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Spin and orbital currents in M2 32S
E, MeV
F
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q-dependence of M2 peaks
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Summary• In the PCC version of SM distributions of the ”hole”
among the (A-1) nuclei states are taken into account in microscopic description of multipole resonances in sd-shell nuclei using spectroscopy of pick-up reactions.
• The energy spread of final nuclei states is the main origin of the multipole resonances fragmentation in open shell nuclei. Comparison of PCC SM results with experimental data on MR confirms the validity of this approach for a range of momentum transfer from “photopoint” up to q≈2 Fm-1.
• The assumption that some very valuable information on MR in excited deformed nucleus is embedded in direct reactions spectroscopy data proved to be right.