Shape parameterization

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Damian Hensley
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1 Shap paatization λ ( θ, φ) α ( θ ) λµ λµ, φ λ µ λ axially sytic quaupol axially sytic octupol λ α, α ± α ± λ α, α ±,, α, α ±, Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

2 Octupol collctivity coupling Δl Δj (W.u.) 6 88a 8 B 6 9 Z ( E; ) 6.H. Spa At. Data an Nucl. Data Tabls (989), so subshlls intact via th opato.g. in light actini nucli on has an intaction btwn j / an g 9/ nuton obitals i / an f 7/ poton obitals Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

3 Octupol collctivity Octupol colations nhanc at th agic nubs:, 6, 88, Micoscopically Intu obitals of opposit paity an ΔJ, ΔL clos to Fi lvl 6 a clos to Z88 N f i ν g ( ) ( ) 7 / / 9/ j/ Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

4 Octupol collctivity 6 a 6 a In an octupol fo nuclus th cnt of ass an cnt of chag tn to spaat, cating a non-zo lctic ipol ont. Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

5 Hans-Jügn Wollshi - 7 Inian Institut of Tchnology opa Th oubl oscillato ( ) ψ ψ ψ ψ E a a V B H -a a V V ω ω ω ν ω V vn vn V E ω ω ω ν ω V o o V E Mzbach uantu Mchanics octupol fo octupol vibational

6 oulob xcitation ipact paat scatting angl σ i f c P i f σ uth c ( E; I I ) f ( η ξ ) [ b] A A σ E.89 EMV B i f E, A Z Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

7 Scatt α-spctu of 6 a H 6 a E α 6 MV θ lab counts - 6 a-tagt ba iction Si-tcto channl nub ( ) [ ] λ / λ λ M Eλ b λ (xp) λ (tho) P i f σ σ i f l θ σ σ i f uth.7 ().6 ().6. (). ().. (7). (8).96 Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

8 Scatt α-spctu of 6 a H 6 a E α 6 MV θ lab counts - 6 a-tagt ba iction channl nub Si-tcto θ ( ) [ ] λ / λ λ M Eλ b λ (xp) λ (tho).7 ().6 ().6. (). ().. (7). (8).96 I f I n I i E E E Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

9 Expintal st-up ϕ ϑ PPA ing count Θ L, φ L 6 6 a PPA count Θ L 9, φ L 8 6 ab ( μg/c ) on -backing ( μg/c ) an cov by B ( μg/c ) Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

10 oulob xcitation of 6 a Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

11 γ-ay spctu of 6 a 8 Pb 6 a E lab.7 AMV counts θ lab φ lab 6 ngy [kv] Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

12 Signatu of an octupol fo nuclus ( ) [ ( θ ) ( θ ) ( θ )] θ : : a E E Singl otational ban with spin squnc: I, -,, -, xcitation ngy E ~ I (I) coptition btwn intaban E an intban E tansitions E tansition stngth - W.u. Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

13 Signatu of an octupol fo nuclus Engy isplacnt δe btwn th positiv- an ngativ-paity stats if thy fo a singl otational ban δ E ( I ) E( I ) I E fo ( I ) E( I ) igi oto W. Nazawicz t al.; Nucl. Phys. A (98) Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

14 Elctic tansition quaupol onts in 6 a ngativ paity stats positiv paity stats igi oto ol: ( I ) I I M ( E) I I liqui op: Z ( ) [ f ] 967 (xp) 7 f. (tho) 68 f H.J. Wollshi t al.; Nucl. Phys. A6 (99) 6 W. Nazawicz t al.; Nucl. Phys. A67 (987) 7 Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

15 Static quaupol onts in 6 a ngativ paity stats positiv paity stats igi oto ol: ( I ) I ( I ) ( I ) ( I ) ( I ) ( E) I ( E) S M I M igi tiaxial oto ol: s ( ) 6cos( γ ) 7 9 8sin ( γ ) H.J. Wollshi t al.; Nucl. Phys. A6 (99) 6 Davyov an Filippov, Nucl. Phys. 8, 7 (98) Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

Elctic tansition octupol onts in 6 a liqui op: Z 7 (.8. 769) [ f ].8..6 ω. MV. I 7 -. ω.mv I ( I ) ( I ) ( I ) ( I ) I M ( E) I ( I ) I ( I ) ( I ) ( I ) I M ( E) I.

16 Elctic tansition octupol onts in 6 a liqui op: Z 7 ( ) [ f ].8..6 ω. MV. I 7 -. ω.mv I ( I ) ( I ) ( I ) ( I ) I M ( E) I ( I ) I ( I ) ( I ) ( I ) I M ( E) I I I I H.J. Wollshi t al.; Nucl. Phys. A6 (99) 6 W. Nazawicz t al.; Nucl. Phys. A67 (987) 7 Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

17 Intinsic lctic ipol onts in 6 a liqui-op contibution: with A Z (. ) 8. [ f] igi oto ol: I M ( E) I I H.J. Wollshi t al.; Nucl. Phys. A6 (99) 6 G. Lan t al.; Nucl. Phys. A (986) 8 Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

18 Intinsic lctic ipol onts in a / Th liqui-op contibution: with A Z (. ) 8. [ f] Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7 G. Lan t al.; Nucl. Phys. A (986) 8

19 Hans-Jügn Wollshi - 7 Inian Institut of Tchnology opa nt of ass consvation τ τ τ τ y x z o Th cooinats (x, y, z) can b xpss by ( ) ( ) ± ±, iy x z φ θ ( ), τ φ θ * * * 6 α α α ( ) ( ) / * * * 6 α α α ( ) ( ) / * * * α α α Th ipol cooinat is not an inpnnt quantity. It is non-zo fo nucla shaps with both quaupol an octupol gs of fo. { } / 7 9

20 Hans-Jügn Wollshi - 7 Inian Institut of Tchnology opa Intinsic lctic ipol ont ( ) z p poton φ θ τ, Th local volu polaization of lctic chag can b iv fo th quint of a iniu in th ngy functional. (Mys Ann. of Phys. (97)) ( ) V nuton poton nuton poton wh p an n a th poton an nuton nsitis, is th volu syty ngy cofficint of th liqui op ol an V is th oulob potntial gnat by p insi th nuclus ( < ) ( ) Z V ( ) n p V p n ( ) V p Kping th cnt of gavity fix, th intgal 9 ( ) 7 Z V

21 Hans-Jügn Wollshi - 7 Inian Institut of Tchnology opa Intinsic lctic ipol ont ( ) ( ) V φ θ, Z A 7 8 ( ) ( ) [ ] ( ) ( ) [ ] ( ) [ ] ( ) [ ] ( ) [ ] Z A ( ) [ ] ( ) [ ] [ ] ( ) [ ] [ ] Z A

22 Hans-Jügn Wollshi - 7 Inian Institut of Tchnology opa Intinsic lctic ipol ont 7 9 Z A 7 6 Z A [ ] f Z A. MV

23 Suay singl otational ban fo I > no backbning obsv,, foation paats a in xcllnt agnt with calculat valus octupol foation is th tis lag than in octupolvibational nucli qual tansition quaupol onts fo positiv- an ngativpaity stats static quaupol onts a in xcllnt agnt with an axially sytic shap lctic ipol onts a clos to liqui-op valu ( I > ) octupol foation ss to b stabiliz with incasing otational fquncy Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

24 oulob xcitation of 6 a 6 a tagt bokn aft 8 hous histoph Flischann Inian Institut of Tchnology opa Hans-Jügn Wollshi - 7

Mon. Tues. Wed. Lab Fri Electric and Rest Energy

Mon. Tues. Wed. Lab Fri Electric and Rest Energy Mon. Tus. Wd. Lab Fi. 6.4-.7 lctic and Rst ngy 7.-.4 Macoscoic ngy Quiz 6 L6 Wok and ngy 7.5-.9 ngy Tansf R 6. P6, HW6: P s 58, 59, 9, 99(a-c), 05(a-c) R 7.a bing lato, sathon, ad, lato R 7.b v. i xal