Systematic of Giant Monopole Energy and the Isotopic Dependence. D. H. Youngblood H. L. Clark Y. Tokimoto B.John

Transcription

1 ---~~~ ~ ~----- Systematic of Giant Monopole Energy and the sotopic Dependence Y. -We Lui D. H. Youngblood H. L. Clark Y. Tokimoto B.John Cyclotron nstitute Texas A&M University

2 Nuclear matter compressibility is a important physical quantity. Supernova Collapse. Neutron Stars. Medium and high energy heavy ion collision. Properties of nuclei. Testing nuclear model from experimental results '

3 The compression modulus of nuclear matter is defined by K =9 2d2E/A =ed2e/a nm Po dp2 no f dk} kro where nois the equilibrium density and kjd is the equilibrium Fermi momentum. One cannot measure this quantity directly. However, one can measure the energy of the compression mode giant resonance such as the isoscalar giant monopole resonance EGMR, which can be related to the compression modulus for the nucleus of mass number A by the following formula fl2 AKA EGMR= 1 m<r2 > Where m is the nucleon mass.

4 K5 Superconducting Cyclotron - 24 MeV a Beam analysis System(BAS)- to obtain high resolution and very clean beam from the cyclotron Broad Range Spectrometer(MDM)- multipoledipole-multipole, able to measure large range of excitation region ( 6MeV). Raytrace Detector - high resolution, able to measure both e (horizontal) and <>(vertical).

5 K5C). CYCLQTRON. '#. " BEAM ANAL1:S1S.~y~fJ:.i\.f;

6 Primary Beam Multipole> Magnet MDMFocal Plane Detector (Top~ew) Faraday Cup (Beam Stop) --- Resistive Wre Proportional Counters (x-pos,e) Scntillator Vertical Driftp'lanes (y-pos, cp) (Side View)~ ~--===i+ x8 R.18tve Wre Proportional COunter Vertical Drift Planes Linear Drift Region onization Chamber lode

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9 OZr J! ; 15 U, g= g=1.8 a a Ex(MeV) 35 4t A 116Sn 3 25 J! 2 c: " U a a Ex(MeV) OOO 15 /1uA\ 144Sm J! c: " u 1 5 a a Ex(MeV) f\ 28Pb 3 25 J! c: " 2 U a a Ex(MeV)

10 8/23/24 4: 13 PM cclresults.xls Figure 1 Youngblood et at Cd 9= 1.1 'tj :i 2 >- 1,, ',,,, Cd 9=3.5 'a Q; 4 > Ex(MeV)

11 4 3 11OCd 9= 1.1 ".! 2 > 1,,, Cd 9=3.5 'tj 'i) 4 >= Ex(MeV)

12 TAMU l! 1 C ::::: U 116Sn(a,a') Ea.=24 MeV 6avg= Ex(MeV) 4 -tn C::s 3 8avg=O.9 2 CJ Ex(MeV)

13 (a) 2 ' J!! 'Si(a,a;').. E..=24 MeV., Ex(MeV) (b) 18 t J!! 1 8 1m /1.1 ''-w Ex(MeV) oo 12. (c) 1 J!! c 8 ::J Pl\.fll Ex(MeV) "" 2 (d) 15 J!! c ::J 1 1\.lll\;T Ex(MeV)

14 Analysis Techniques Slice analysis (multipole decomposition) All multipoles (L = to 4) The multipole components of the giant resonance peak were obtained by dividing the peak into multiple regions (bins) by excitation energy and then comparing the angular distributions obtained for each of these bins to DWBA calculations. The same analysis applied to the continuum, but only the L=O components was included to the total strength. The resolution of the bins varied from 15 key to several MeVs.

15 New: Choose a continuum and subtract it. Divide the remaining peak AND the continuum into 1 MeV wide bins. 6 -> Q) 5 ::2:... U) 4 -..c E 3 9Zr(a,a') Ea;=24 MeV ec.m.=1.ao GR peak "sliced" into MeV bins for multipole decomposition analysis... W "'C C 2 "'Cb 1 N "'C Ex (MeV) Fit the resulting angular distributions with a sum of isoscalar EO, El, E2, E3 and E4 strength. nclude the known isovector El strength. 1 :f ~ 15<Ex<2 MeV t T.~ ~1 t --~'".c :[: g c 32 t t ~ 1 t tt L=O, T=J m- L=2.'\~\.':'.;;;<:\. '\, / \. '. "~ \\ \>oj!", Oc.m (de g) & 1.c g c: =B 1:1 _n L=O "'.. "' "' " '\ 2<Ex<25 -MeV..., ' -', ---, ',, \,,, \, ",,, '',j, \ - L=3 +--t O. -L=1,. T=O v Oc.m.(deg) [ i Becau~e of the strong FORWARD PEAKNG of the EO angular distribution can identify the EO strength in the peak AND in the "continuum". Actual EO strength distributionup to Ex ~ 4 MeV. No particular shape is assumed! EO strength obtained is independent of continuum choice.

16 DWBA Calculations - extract % EWSR Folding calculations Density dependent gaussian with Woods- Saxon imaginary term (Khoa and Satchler)

17 The folding model approach to the potentials is more basic and provides a direct and unambiguous link between the potentials and the underlying nuclear densities. n this approach, the potentials are generated by folding an effective nucleon-nucleon interaction over the density distributions of the target and projectile. The results from this approach can be very different to those obtained from the deformed potential model. n our calculations, we use a hybrid folding model, in which real potential: density dependent, single folding with Gaussian shape. Ua(S) = -uexp(-s2 /t2),s = ; -;11 UDDG(S,P)= ua(s)f(p),f(p) = l-a(l + j3)p(rl)f3 imaginary potential : Woods-Saxon shape mu(r) = -w /(ex + 1), x = (r - Rw)/ aw This model was used successfully to analyze the 24 MeV a data on 58Nias an initial test case by G. R. Satchler. G. R. Satcler and Dao T. Khoa, Phys. Rev. C 55, 285(1997)

18 Single folding: average the interaction over the density distribution of the a particle. use the same radial shape for both real and imaginary potentials, this results too strong absorption in the interior. set imaginary potential to Woods-Saxon shape. Density dependent: the strength of real interaction required To fit small angle scattering is too deep in the interior to reproduce correctly the rainbow features at large angle. making interaction between a particle and target nucleon depend upon the density of the nuclear matter. reduce the strength of the interaction as the density increasing, weakening the folded potential in the interior while leaving the peripheral values largely unchanged. Gaussian shape: good fit to elastic data.

19 Transition density go(r) = -a;[3pt(r)+r dp~r)] for GMR g~m(r) = -t5t dpt(r) dr for ~ 2 pt(r) is the ground-state density of the nucleus t5t is the corresponding matter deformation length G. R. Satchler, Nucl. Phys. A472, 215(1987). /31 2 d 5/ 2 ) d d2 d gl(r) = -- R 3r -+lor--{ -+t: r-+4- Pt [ dr 3 dr ( dr2 dr J] for SGDR n 4 5 t:= ( E2 + Eo J 3mA where E2 and EO are quadrupole and monopole energies. M. N. Harakeh and A. E. L. Dieperink, Phys. Rev. C 23, 2329(1981).

20 Folding model analysis of 24 MeV alpha scattering U(r) =-v!p(r')f(p)exp(-s2/f) d~ - vw/(1 + exp(r-rw)/a,.) 1.E+7 where: f(p ) = 1-ap(r')f3, a=1.9 fm2, t=1.88 fm and 13=213 1.E+6 1.E+5 9Zr X 16 1.E+4.c- ::J a: J2c. 1.E+2 x Q) b t.oe+3 116Sn X 14 1.E+1 144Sm X 12 1.E+ 1.E-1 28Pb 1.E-2 1.E e em (deg)

21 ---~~-- ~ Folding model analysis of low-lying states: Calculations made using "electromagnetic values" for B(E O8Pb X 14, J"=3-, Ex=2.61 MeV 1 ~1oo :c g " a 1 t5 ".1 9Ozr, J"=3-,Ex=2.75MeV 144Sm x 12, J"=2++3-, Ex=1.66MeV ecm (deg) 'C" tn :D 1 E-a 1165n«1,<1') J"=2+, Ex=1.29 MeV x 12 " b " J"=3-,Ex=2.27MeV ac.rn.(deg)

22 S\ t c..e-""y s1$- '\"' cer1'.141: T=o t..:, L&C> M ft MeV 'C" :c.5.1 a :!:! b " MeV ry 1 \ ' c.m.(deg) 9c.m.(deg) 1 1 "i:" 1/ MeV -..- :a :a E.5.1 C a " b b " " 1 1 J \ c.m.(deg) 9c.m.(deg) MeV.. 'C" :c :c a a :!:! :!:! b b " " c.m.(deg) 9c.m.(deg) MeV 'C" -.. :c :c a a :!:! " " b " b MeV c.m.(deg) 9c.m.(deg) MeV MeV.. 'C" :c :c a a :!:! :!:! b b " " 5 9c.m.(deg) c.m.(deg)

23 8/23/24 5:13 PM, " S,.(rJ.,d. ) Figure3 LUJETAL. 1 'i:" f) :is.5.1 a ~" Peak 12.2 MeV Continuum 1 1 'i:".!!.a.5.1 a"5 " 16.2 MeV !!.a.5.1 a"5 " MeV c.m.(deg) L= c.m.(deg) 1

24 823l2OO4 4:3 PM cdresulls.xls Figure 3 Youngblood at al iii: t Cd EO c 'g.1!! L ExCMeV).61 rt 9i.4 3:: w c.2 U!.2. NRr T T r rt E EJMeV) :.2 E2.15 w c.2 U.1.! EJMeV).1 1 E3 t:.8 w c.6.2 U! EJMeV)

25 823l2OO4 5:fJ7 PM Fi~5Ll.ietal-

26 9Zr.25,.2 i.15 iii iii c:.1 ED i&..6 i li1 i.4 E :Jo is.1 : Ji! 1:1 &: E2 ).1 m.os c: E3 ) S Ea(eV)

27 .12.1 T: ~.8 c~ :8 ::.6 uti) ~3: LL wo Ex(MeV) 56Fe EO EWSRlMeV (m3/m1) 1/2= Me >.7 wc ~ 41.6,.2 ::.5 -t) E 3:.4 LLwO Ex(MeV) 58Ni EO EWSRlMeV (mim1) 1/2= MeV >.7 ~ ~.6.2 ::.5 -t) E 3:.4 LL wo Ni EO EWSRlMeV (m3/m1)1/2= MeV Ex(MeV) T: ~.6.2 ~.5 ~ ~.4 LL wo Ex(MeV) 64Zn EO EWSRlMeV (mim1)1/2= mev.71 35

28 1/11/1 1:2' AM c:\documents\21 pro\brookhaven\figs.xls.5iprc(in ~.4 :E ii U) ~.3 w w c.2 ~.1! press) % dp Ex(MeV) > CD :i! ii.1 U) ~ w w c.2 UtS.5 t U... PRC(Submitted 7/1) 28S % PRC63,6731 (21) 25 Ex(MeV) > CD!! ~ ; w.5 w c ~.. 4Ca % u Ex(MeV) 35 45

29 4/28/98 4:15 PM gmrsys.xls Texas A&M, Knm obtained by comparing GMR energies and RPA calculations [Blaizot et al. NPA591,435(1995)]. Go, uy u4,at4c.i1-s :> C>23 - Ec """"J:""" 4Ca <>TAMU 1998 <>World 1993 ~ 9Zr i 1165n Knm= MeV ~. 1445m 28Pb A plil.. t!., &q (( 99V

30 KAcan be expanded in volume, surface, symmetry, coulomb and higher order contributions in the following K - K K A -113 K ( N-Z ) 2 K Z2 A - vol +~. surf + sys A + caul A4/3+... Rely on n1icroscopic calculations to provide consistent determination of monopole energy and the nuclear matter parameters.

31 3 Giant Monopole Energies Using (a,a') at 24 MeV ~ 22 ~-~ E 2 ~ Experiment -8*A-1/3 -t:r- Nayaket al. SkM* A

32 Nayak et al. Nucl. Phys. A516, 62 (199). Within the framework of the scaling model, four different Skyrme-type forces, using extended Thomas-Fermi (ETF) approximation. SkM* (Knm=217MeV),RATP (Knm=24MeV) Michel Farine, J. M. Pearson, F. Tondeur, Nucl. Phys. A615, 135 (1997). Generalized Skyrme-type forces with a term that is both density- and momentum-dependent. Semiclassical with corrections (no RP A). Fit EGMR. Knm ~ 215:f:15 MeV T. v. Chossy and W. Stocker, Phys. Rev. C 56, 135 (1997). Parameter sets in nuclear relativistic mean-field theory. Knm< 23 MeV

33 35 3 >' 25 <U ~--- ~ ~ /3 KA=Kv+KsfA +Kvs[(N-Z)/A]+KcoulZA +small term R. C. Nayak et al., Nuel. Phys. A516, 62 (199) T. v. Chossy and W. Stoker, Phys. Rev. C 56, 2518 (1997). EXP - 8A1\(-1/3) - Nayak_SkM*(KV 216.6) - Nayak_RATP(KV=239.5) -- Nayak_SkA(KV=263.1) - Chossy_NL-Z(KV=172.8) -Chossy_NL1 (KV=211.1) - Chossy_NLC (KV-224.5) A

34 - ~ 17 if -~ E 16 ls Nayak et at NPA516,62(199) SkM* 217MeV - Experiment ~S~~ GMR Energy -Chossy&Stocker NL PRC56,2518(1997) A 18 -, i L Cd sotopes 15 GMR Energy -+- Nayak et al. NPA516,62(199) SkM* - Experiment -Chossy&Stocker PRC56,2518(1997) NL : A

35 :> 1.3 a> ::E-w 1.1 cu Ḡi "C.9 TAMU 24 Energy Difference 1125n-1245nGMR _RMF -+- Non-Relativistic -Experiment Modified Skyrme Knm(MeV) :> a> ::E-w.5 Energy Difference CdGMR -RMF -+- Non-Relativistic -Experiment ModifiedSkyrme cu Ḡi "C Knm(MeV) 37

36 n the past few years, high precision experimental data on giant resonances have been obtained from 12C to 2 8Pbusing 24 MeV a particles from the Texas A&M K5 superconducting cyclotron..1% EO EWSR in heavy nuclei such as 9Zr, 116Sn, 144Smand 2 8Pbhave been found..n light nuclei, nearly 1% EO EWSR in 4Ca,28Si and 24Mg,and 5% EOEWSR in 16 have been located..using 2 8Pb, 144Sm, 116Sn, 9Zr and 4Ca data a nuclear matter compressibility of231:!:5 MeV is obtained by comparing microscopic calculations using Gogny interaction..mass dependence using Leptodermous expansion..study the symm~try effect by measuring Cd and Sn.

37 Conclusions.n 112Snand 124Sn,predictions using relativistic and non-relativistic (Skyrme or Skyrme-like) interactionswith Knm ~ MeV result in energies. consistent with the experimental energes..n 11Cdand 116Cd,they are slightly above the experimental energies..n more accurate energy difference between the EO position in 112Snand 124Snis consistent with relativistic calculations for the NL-C parameter set (Knm=224.5MeV) and with calculations using modified Skyrme interactions having Knm=22 and 24 MeV..Also it is true in energy difference between 11Cdand 116Cd.

38 Using Leptodermous expansion to extract Nuclear Matter Compressibility. High Risk!! Need to be careful!! Wrong!! What really needed is "REAL" Microscopic Calculations for these Nuclei.