Magnetic dipole and quadrupole response of nuclei, supernova physics and in-medium vector meson scaling

NUCLEAR PHYSICS A ELSEVIER

Nuclear Physics A 606 (1996) 183-200

Magnetic dipole and quadrupole response of nuclei, supernova physics and in-medium vector meson scaling * C. Ltittge 1, R von Neumann-Cosel, F. Neumeyer, A. Richter Institut fiir Kernphysik, Technische Hochschule Darmstadt, D-64289 Darmstadt, Germany

Received 10 May 1996

Abstract The relevance of magnetic dipole and quadrupole strength distributions for the physics of a type II supernova are discussed. A recently developed high-resolution, large solid-angle system for the detection of 180° electron scattering at the superconducting Darmstadt electron linear accelerator (S-DALINAC) is introduced which represents a unique tool for the study of low-multipolarity magnetic transitions. First results discussed include the modification of the M1 strength in complex nuclei by meson exchange currents, the overall quenching of M2 strength and possible tests of in-medium vector meson scaling (Brown-Rho scaling) by selected magnetic form factors. Keywords: M1 and M2 strength distributions,Relation to supernovaphysics, Quenching,Exchange currents,

180° electron scattering, In-mediumvector meson scaling

1. Introduction The contributions of Gerry Brown to nuclear physics span the whole range from low-energy nuclear structure (remember the seminal papers on the first microscopic description of the electric dipole giant resonance [ 1] and on the derivation of a shellmodel residual interaction from a realistic nucleon-nucleon force [ 2 ] ) up to quark effects in nuclei (see e.g. Ref. [3] ). In this contribution for Gerry in honour of his 70th birthday we want to discuss a few examples of how our subject of interest here - the magnetic dipole and quadrupole response of nuclei at low excitation energies extracted * Dedicated to Gerry Brown on the occasion of his 70th birthday. l Present address: DESY, D-22603 Hamburg, Germany. 0375-9474/96/$15.00 Copyright @ 1996 ElsevierScience B.V. All rights reserved Pll S0375-9474(96)00199-6

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from electron scattering - has been fructified by Gerry's ideas, and how these classical nuclear structure investigations may provide unexpected insight into some questions which seem quite distinct at first hand to low-energy nuclear physics. The first example we pick from astrophysics. It is well known that the fate of a massive star in the late stages of his evolution is strongly influenced by the spinisospin response of nuclei, i.e. by Gamow-Teller (GT), respectively M1, and unique first-forbidden (UFF), respectively M2 transitions, as well as their total amount of quenching [4]. Another example constitutes the sensitivity of certain transverse electron scattering form factors to modifications of the vector meson coupling in the nuclear medium [5] which might even allow to test the 'universal scaling' law for effective nucleon and meson masses by Brown and Rho [6]. This note is organized as follows. After a brief (and necessarily far from complete) summary of the relation between low multipolarity magnetic transitions, electron capture in presupernova stars and nucleosynthesis during the supernova shock wave in Section 2, a new 180 ° electron scattering system recently installed at the S-DALINAC is introduced in Section 3. First examples of measured M1 and M2 strength distributions and what can be learned from them are presented in Sections 4 and 5. Section 6 discusses an example of the effect of in-medium vector meson scaling on magnetic form factors, and finally Section 7 gives a short outlook on our future program.

2. The role of M1 and M2 strength in supernova physics The hydrodynamics of stellar collapse leading to a type II supernova has been a central topic of Gerry's work in the last one and a half decades. In the pioneering paper by Bethe, Brown, Applegate and Lattimer [7] it was shown that the two most important quantities determining the fate of a massive star are the entropy per nucleon and the lepton-to-baryon fraction. The latter, in turn, is influenced by electron capture (and fl-decay) rates in various ways. One aspect is that the final core sizes preceding the gravitational collapse are sensitive [8] to the degree of neutronization via the reaction (I)

p + e - ---~ n + ue

on free protons as compared to the reaction in nuclei (N,Z)

+e-

~

(N + I,Z-

1) +v~.

(2)

The energy distribution of the weak interaction matrix elements is unknown for most cases relevant to presupernova stars and collapsing cores (mostly fp-shell nuclei). However, such information can be derived from the corresponding GT strength distributions. In fact, the need for their precise knowledge in astrophysics has been a strong motivation for extensive experimental efforts to study (p,n) and (n,p) charge exchange reactions at incident energies of a few hundred MeV and small momentum transfers (see e.g. Ref. [9] for a recent review).

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On the other hand, some progress has been achieved recently theoretically in the attempts to find systematical parametrizations of the GT strength beyond the oversimplifying single-particle model used in astrophysical network calculations so far [ 10]. Koonin and Langanke [ 11 ] demonstrated that the total GT+ strength in fp-shell nuclei exhibits a simple functional dependence on valence nucleon numbers, and Ref. [12] reports a description of the GT spectra by spectral distribution theory. It was also recognized by Brown and others [13] that previously unconsidered electron capture and /3-decay of nuclei with A > 60 becomes important in the very last stages of stellar evolution. In order to see the relation between the M1 and the GT strength the GT operator can be written in the notation of Bohr and Mottelson [ 14] as /z+(GT)=

ga V~

A So_t~(j)t±(j) j=l

'

(3)

where gA denotes the axial vector coupling constant, o-u(j) are the spherical components of the spin operator and T+ = ~.i t± (j) is the isospin ladder operator. The GT operator has no direct counterpart among the electromagnetic moments. However, the isovector part of the one-body M1 operator /x(M1) =

[4.7. o-~(j) + 1 - l , ( j ) ] t 3 ( j ) t x N

(4)

j= 1

is dominated by the spin term and the matrix element of the latter is directly related to the GT matrix element. The connection between GT /3-decay and M1 strength is obviously slightly complicated by the presence of isoscalar and orbital contributions (though the former are small). Nevertheless, the nuclear MI response is a fundamental test of all microscopic models aiming at a description of the magnetic properties of nuclei and in many realistic cases the corrections due to orbital currents are small. In particular, the total amount of quenching of M1 and GT strength, which also enters into the astrophysical modeling, constitutes a fundamental and still unsolved problem where experimental investigations of the magnetic dipole strength are of vital importance (see e.g. Refs. [15,16] and references therein for a discussion of the famous example of the transition to the Ex = 10.23 MeV, J~" = 1+ state in 4SCa). During the gravitational stellar collapse the inner core nuclei become so neutron rich that allowed electron capture is strongly suppressed because of Pauli blocking of the relevant outer shells [ 17] and first-forbidden transitions involving states with J~ = 0 - , 1-, 2 - gain importance. For the UFF transitions there is a direct correspondence to the spin-isovector magnetic quadrupole matrix element M,~(M2) 7 5 / z _ (Gl)/z N fm, M~(M2) - 2¢r T> where/z_ =4.7 as in Eq. (4) and (Gi) denotes the/3-moment [18].

(5)

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C. Liittge et al./Nuclear Physics A 606 (1996) 183-200

I

I

UFF

I

I

J3- d e c a y a n d M 2 t r a n s i t i o n 0 []

0.6

131

I

[3 -decay (e,e')

0.4

C~

+

0.2

0

//

I

I

0

0.2 Relative

I

I

_

I

0.4 0.6 0.8 Neutron Excess

Fig. I. Renormalization of the axial vector coupling constant gA in UFF/3-decays and analogue M2 transitions. The dashed line is a calculation with a multipole-multipole force from Ref. 1211 and the solid line from Ref. 1201 who additionally took higher order core polarization and AN--I coupling into account.

The effects of first-forbidden transitions were investigated by Zaringhalam [ 19] and by Cooperstein and Wambach [20]. The latter included excited state distributions which are thermally populated at the high temperatures in the presupernova environment. Since e - capture proceeds preferentially at low Q-values, the coupling constants g a , g v are considerably renormalized due to particle-hole (p-h) correlations. Fig. 1 presents reduction factors of ga extracted from measured UFF/3-decays (open circles) compared to the predictions of a multipole-multipole force calculation by Ejiri [21] shown as dashed line. The renormalization factors are plotted as a function of the neutron excess given in units of the number of nucleons per ho) harmonic oscillator shell. The predictions of the calculations still have to be lowered by including correlations due to higher order core polarisations and A N - 1 excitations as done in the approach of Ref. [20] shown as solid line. The open squares are quenching factors extracted from M2 transitions in 42'44Ca analogue to the 42"44K ground state observed in electron scattering [22]. They are in good agreement with the predictions of Ref. [20] indicating that orbital contributions play a minor role. With the new experimental device described in the next section such electron scattering studies could be extended to other analogue M2 transitions of astrophysical interest (e.g. in J4C and 4°Ar) and also to M3 transitions (e.g. in 26Mg, 28Si, 52Cr, 56Fe). Finally, the distribution and total strength of M1 and M2 giant resonances play an important role in the u-nucleosynthesis process [23]. The extremely high neutrino fluxes emitted during a supernova explosion lead to non-negligible rates of inelastic neutrino scattering on nuclei in the outer shells of the star. Numerical calculations indicate [24] that the neutrino scattering cross sections are dominated by the MI, E1 and M2 re-

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sponse functions. Since the major part of their strengths lies above particle threshold new isotopes can be produced by neutrino excitation and subsequent continuum particle emission. A detailed modeling [25 ] indicates that this process should contribute significantly to the nucleosynthesis of light (Li, Be, B) and some exotic heavy (J38La, 18°Ta) isotopes. In passing we note that lS°Ta - nature's rarest isotope and the only naturally occurring isomer - may be a prime candidate for pure u-process production [26]. In any case the relevant magnetic strength distributions, which form an essential input for a realistic description, are not known for most nuclei and need to be measured in the near future. Since the S-DALINAC [27] is still the only remaining low energy electron accelerator in the world in times of a great rush to higher and higher energies, great experimental effort will clearly be devoted to this fundamental problem.

3. H i g h - r e s o l u t i o n

180 ° electron scattering at the S-DALINAC

- a new tool for

investigations of the M1 and M2 response

A particular attractive experimental tool for the investigation of magnetic transitions in electron scattering is a detection system capable to measure at 180 °. There, the longitudinal part of the inclusive (e,C) cross sections essentially disappears while the transverse contribution remains finite. Thus, magnetic transitions - which are of purely transverse nature - are strongly enhanced at 180 ° where the elastic radiative tail is largely suppressed. Recently, a new system for high-resolution 180 ° electron scattering has been installed at the S-DALINAC. The layout is drawn schematically in Fig. 2. The incident beam is deflected 25 ° by a chicane and redirected to the original beam direction with a magnet placed in the center of the scattering chamber. The target position is moved downstream, and the electrons scattered by 180 ° are deflected by the same separating magnet into the magnetic spectrometer. A system of quadrupole lenses and Helmholtz coils prevents electrons back-scattered from the Faraday cup to enter the spectrometer. The system was brought into operation in 1994 and first experiments were immediately successfully conducted. Compared to previous 180 ° systems the present device shows a number of exceptional features [28] because of the coupling of the system to a large-aperture, large-momentum-acceptance QCLAM magnetic spectrometer [29]. The properties of the new system can be summarized as follows - maximum central momentum 95 MeV/c, - momentum acceptance - 5 % to +8%, - horizontal and vertical opening angles 40 mrad, - solid angle acceptance 6.4 msr, - intrinsic momentum resolution 2 x 10 -4. Typical values of older systems were horizontal acceptances of ±15 mrad and solid angles of about 1 msr. The central momentum range is sufficient for the observation of M1, M2 and M3 transitions. The maximum value of 95 MeV/c roughly corresponds to the first maximum of a M3 form factor.

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188

to Faraday Cup

Deflecting ~

0

lm

~

o

"~ Incident Beam

Fig. 2. Schematiclayout of the 180° electron scatteringsystem at the S-DALINAC.

The detector system of the Q C L A M spectrometer consists of three multiwire proportional chambers, two measuring in dispersive and one in vertical direction, a plastic scintillator serving as a trigger and a large Cerenkov counter for background suppression. With the information of the drift chambers a complete track reconstruction is possible. This allows e.g. to distinguish directly between electric - which also may have transverse cross section parts - and magnetic excitations by looking at the angular distributions over the horizontal or vertical opening angle [28]. In a first experiment the magnetic dipole and quadrupole response of 28Si up to an excitation energy Ex -~ 19 MeV was investigated. This experiment already demonstrates the power of the new 180 ° system operated in conjunction with our excellently performing continuous wave superconducting electron accelerator S-DALINAC. Fig. 3 shows a spectrum taken at E0 = 50 MeV. Note that the excitation energy range of 9 to 19 MeV was covered with two spectrometer settings only. The multipolarity assignments demonstrate impressively that 180 ° electron scattering serves as a 'spin filter'. Numerous magnetic (marked by an arrow), but only two rather weak electric transitions (not marked) are observed. We next list and discuss a few salient features of the measured M1 and M2 strength distributions in 28Si.

4. Isovector magnetic dipole response in 2SSi and the role of meson exchange currents It is well established in sd-shell nuclei that full 0hw shell model calculations are able to describe the total MI and GT strengths (except an overall quenching of the

C. Liittge et al./Nuclear Physics A 606 (1996) 183-200

189

+ o o ~ +°°I

I

+L &

° =++°i

'[ II '('['i '('(i-i - 'i 'iJ-++i

2 0 0 ~-3+

3+ '+

+ t

2-

z

1" 2-

1+

2-

2-,3 +

3+

+fill 11 lily, Ill l l!

100

0 10

12

14

16

18

Excitafion Energy (MeV) Fig+ 3. Spectrum of the 28Si(e,e ~) reaction under 180 ° for E0 = 50 MeV. Only lines due to magnetic excitations are denoted by an arrow. ~ free x spin g-factor throughout the sd-shell by geft"= u.sgs ) while details of the distributions might be missed. In Fig. 4 the running sum of the B(M1 ) strength extracted from our 28Si(e,e t) experiment [30] is plotted. The dashed line corresponds to a shell model calculation with the 'unified sd (USD)' interaction of Brown and Wildenthal [ 31 ] with

10

'

I

I

'

'

I

'

' j~

28Si(e,e') 8

I

--

J

Eo = 4 2 - 6 2 MeV

z

:::k 6

r///////~ I F/1/IliA _

A

re,

4

--

,- ............

I

:

'

i

free nucl. g - f a c t o r s

i

2

-' ....

. . . . .

I

!......

Pq

,-

J

I-

..... elf. nucl. g - f a c t o r s I

0 10

~

12

1

14

i

I

I

16

Ex ( M e V ) Fig. 4. Running sum of the B(MI ) strength extracted fi'om the 28Si(e,e I) experiment 1301. The dashed and dotted lines represent shell model calculations with the USD interaction 1311 with free and effective [36] spin g-factors, respectively.

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C Lfittge et al./Nuclear Physics A 606 (1996) 183-200

free nucleon g-factors. The shell model result with quenched g-factors is displayed as dotted line in Fig. 4. While this calculation yields almost perfect agreement with the GT strength extracted from a 2SSi(p,n) experiment [32], the M1 strength is clearly underestimated. Such an enhancement of the experimental MI strength can be traced back [33] to effects of meson exchange currents (MEC). To make this clear it is convenient to write the M1 and GT strength in the following form B(M1 ) - 3(#p - #n) 2 87r

[M~ + Mt + MA +

MMEC]2 '

B ( G T ) = [M,~ + MA + MMEC] e,

(6) (7)

where Ml and M,~ are the orbital and spin matrix elements, and Ma stands for the contribution of A-isobar admixtures to the strength. The numerical factor before the square brackets in Eq. (7) equals to 2.643/x~ for free nucleon g-factors. Neglecting the orbital part which is at most of the order of 10% in open sd-shell nuclei according to systematic investigations [ 34], the main difference between M1 and GT excitations lies in the MEC contributions, which are of vector type for the former and of axial vector type for the latter. Since axial vector currents are strongly suppressed because of the conservation of G-parity [35], deviations of the ratio R ( M 1 / G T ) = ~ B(M1 )/2.643#~ B(GT)

(8)

from unity point towards an enhancement of the M1 strength by vector type MEC contributions. The results of such an analysis for 2Ssi and 24Mg, which was studied in Ref. [33], are summarized in Fig. 5. While the shell-model calculations using free g-factors predict ratios close to one (differences are due to the small orbital parts), the experimental R ( M I / G T ) are much larger. Taking into account in-medium corrections to the M1 or GT operators determined either empirically [36] or in perturbation theory [37] the model calculations also indicate a clear enhancement of R ( M 1 / G T ) , which e.g. in the approach of Ref. [37] are directly related to the MEC contributions. The remaining difference between the experimental and calculated enhancement of the M1 strength in 2SSi might be due to stronger g.s. correlations than anticipated by the present shell model description [38].

5. Isovector magnetic quadrupole response in 2SSi and the quenching of M2 transitions In Fig. 6 the form factors of the transitions to excited states in 285i at Ex = 11.45 and 14.36 MeV are displayed as examples. Additionally, data from earlier 28Si(e,e/) experiments with the high-resolution, energy-loss spectrometer taken at the old DALINAC are shown as open circles [43,39]. The agreement between the measurements is satisfactory. Clearly, the different muitipolarity of the two transitions (M1, M2) can easily

C. Lu'ttge et al./Nuclear Physics A 606 (1996) 183-200

191

Em G x < 15.5 MeV 2.0 . . . .

calc. eft. g-factors

1.8 (..9

m emp. eft. g - f a c t o r s

1.6

&..,.--

~E £E

t

1.4

--free g - f a c t o r s

1.2 1.0

24Mg

28Si

Fig. 5. Ratio of the total MI and GT strengths defined in Eq. (8) for 24Mg [33] and 28Si [30]. The horizontal bars are shell model results with the USD interaction and free (solid) and quenched (dashed [37], dotted [361 ) spin g-factors.

be determined by inspection of the form-factor dependence on the effective momentum transfer qeff. The theoretical form factor presented for the M1 transition to the Ex = 11.45 MeV level in the 1.h.s. of Fig. 6 is taken from the shell-model calculations described in the previous section [30]. For the M2 transition to the Ex = 14.36 MeV state only a single particle ds/~ --~ f7/2 form factor is depicted, since there exist no shell-model predictions for M2 strength which involves at least lhw excitations. The absence of reliable sets of cross-shell two-body matrix elements prevents any shell-model description of lhw transitions except for the lightest nuclei [40,41]. However, the extraction of M2 transition strengths from low-q electron scattering is largely model-independent for a light nucleus like 28Si, where we deal with isovector excitations only; for the procedure of determining this strength see Ref. [42]. The distribution of B(M2) strength in 28Si extracted from the present experiment is displayed in the lower part of Fig. 7. The upper part shows the results of the previous 28Si(e,e') experiment [43] which measured a smaller excitation energy range only. In the energy span covered by both experiments satisfactory agreement is found. However, the present results indicate that the M2 strength in 2Ssi is spread over a much larger energy interval than previously thought. Significant additional strength is found below

192

C. Liittge et al./Nuclear Physics A 606 (1996) 183-200 I

I

I

I

I

I

M 1 Ex= 11.,5 MeV

I

M2

I

I

I

Ex--,436MeV

¢q

t r 10

-2

10 -3 t~l

I,

t.L

• 180 ° S - D A L I N A C o DALINAC

o DALINAC 10 -4

10 -3 I

0.2

I

I

0.6 q,ff ( f m -t)

I

I

1.0

I

0.2

I

I

0.6

I

I

1.0

q,ff ( f m - ' )

Fig. 6. Form factors of the transitions to the Ex = 11.45 and 14.36 MeV states in 28Si. The solid triangles are from measurements with the new 180° electron scattering system and the open circles are from earlier experiments [39,43 I. The solid lines are a M 1 form factor from the shell-model calculations described in Ref. [30] and for a M2 d~/~ ~ .f7/2 single particle transition, respectively. and above the energy region E× -~ 13-16 MeV covered in the earlier measurements. As a result the total B ( M 2 ) T transition strength more than doubles to 931.2/2Nfm 2, but the average energy of the M2 giant resonance only slightly increases from /~ = 14.6 to 14.9 MeV. A description of the M2 response in nuclei has been discussed within various microscopic RPA and QRPA approaches [ 4 3 - 4 7 ] . Specific predictions for 28Si have been reported e.g. in Refs. [43,48]; the latter, however, showed little resemblance to the data [49]. A matter of special interest is the possible existence of a T = 0, orbital 'twist' M2 mode [47,50-52] first proposed by Ref. [53] which has also been studied in a macroscopic fluid dynamical model [54] based on the concept of elastic nuclear matter [55]. However, in the microscopic models sizeable contributions of this mode to the total M2 response are predicted for heavy nuclei only. Since no model-independent sum rules exist for magnetic excitations the impact o f the above experimental result on our understanding of the quenching of M2 strength - which is far from complete at present - can only be expressed by comparison to some model approach. The retardation o f M2 strength with respect to RPA predictions was discussed already early in Ref. [43] and a common mechanism responsible for the quenching o f all spin magnetic properties was advocated [56], where about half of the reduction is due to core polarization and half due to a mesonic renormalization of the spin current. Here, we compare the existing data on M2 transitions to an energy-weighted sum rule ( E W S R ) by Traini [57] for spin-isospin magnetic multipole strength which is due to

C. Lfittge et al./Nuclear Physics A 606 (1996) 183-200

160

F

r

"i

n

T

r

193

]

28Si 120

DALINAC

80

E 40 7

:::L <--tN

160

28Si S-DALINAC

120

133

80 I I

40 , I

I

I II I II

0 12

14 Ex

16

18

(MeV)

Fig. 7. Lower part: the B(M2) strength distribution extracted from the 28Si(e,e~) experimentwith the 180° system. The dashed lines correspondto transitions which havelikely M2 character,but M3 cannot be excluded. Upper part: results of an older experiment [43] at the DALINAC. a generalization of Kurath's sum rule for magnetic dipole transitions in self-conjugate nuclei [58]. Starting from an evaluation of the double commutator of the magnetic moment operator and taking into account the kinetic energy term, the spin-orbit and the two-body interactions, one arrives at the following description for M2 transitions directly applicable to experiment Z

B ( M 2 ) 1" -Ex = 61.94 [½/z_ - ½12A(l ÷ fl2)/z~fm2MeV.

(9)

The quantity A stands for the nuclear mass number. When estimating the importance of the different contributions one finds that the spin-orbit part, which dominates for M1, is small for higher multipolarities. The parameter/32 in Eq. (9) gives the ratio of two-body over kinetic energy contributions and for realistic Skyrme-type forces takes values [57] of/32 = 0.44 (SIII) and 0.73 (SKA). Fig. 8 summarizes the resulting EWSR predictions compared to the world's M2 data. Except for the lightest nuclei, all experimental results have been obtained in Darmstadt [43,59,60]. So far, the experimental knowledge is restricted mainly to doubly or singly closed-shell nuclei. The summed energy-weighted B(M2) strengths increase smoothly with A (dashed line). Apparently, the new results on 28Si, which is the only open-shell case investigated so far, fit well into the empirical systematics.

C Liittge et al./Nuclear Physics A 606 (1996) 183-200

194

10 6

'

I

.

.

.

I

.

'

'

'

'

I

'

'

'

'

I

. . . .

I

'

'

4OCa 48Ca

C

t

o t'N

I

'

SIllo

Exp.

10'*

tt

* ~

t

160 2+Si

,,,

'

Ska

~

E ~::&z lO s

'

10 3

14OCe

9°Zr

2~pb

A DALINAC

• S-DALINAC ,

I

0

,

,

,

,

I

50

,

,

180 ° ,

,

I

,

,

100

,

,

I

150

,

,

,

,

I

200

,

,

,

j

I

,

250

A Fig. 8. Energy weighted sum rule values of all available M2 strength distributions as a function of mass number. The dashed line is an empirical fit to the data. The dashed-dotted and solid lines represent EWSR predictions of Ref. [57] using two different effective Skyrme forces.

With respect to the model predictions [57] one finds a strong suppression for the heavy nuclei of almost an order of magnitude. The deduced ratio (with the SIlI interaction) for nuclei A ~> 90 is almost constant at a value of 0.19 and then increases towards lighter nuclei up to about 0.68 for 160. While this behaviour qualitatively agrees with the mass dependence of quenching for M1 and M2 transitions with respect to RPA predictions [56] it would indicate a much stronger renormalization of the spin g-factor, i.e. fromg.,.eft (M1) = 0.8gsfree (M1) tog~ff(M2) ~ 0 . 4 g s free (M2). Such a difference would clearly ask for a theoretical explanation. Some comments are, however, in order concerning the experimental results and their interpretation. (i) The experiments on the heavier nuclei all cover limited excitation energy ranges only. Their choice has been guided by predictions of l p - l h RPA using the MSI interaction [61] which probably underestimate the degree of fragmentation and the spreading over a wide excitation energy interval as already indicated by the present experimental results on 28Si. This becomes obvious when 2p-2h and A-isobar effects are taken into account [47]. Furthermore, in heavy nuclei a non-negligible part of the strength is pushed to very high excitation energies [47] contributing with a correspondingly larger weight to the EWSR. Thus, it seems necessary to examine in all cases whether additional M2 strength is found outside the energy regions investigated so far. (ii) The approach of Ref. [57] neglects parts of the M2 strength due to convection currents. As discussed above an isoscalar, torsional orbital M2 mode was predicted [53] for heavy spherical nuclei, and RPA and quasiparticle-phonon model calculations indicate

C. Liittge et al./Nuclear Physics A 606 (1996) 183-200

195

non-negligible contributions to the M2 strength [47,52]. (iii) It can be argued in analogy to the M1 case [35,62] that the in-medium modification of the M2 spin operator should be universal and the reduction of quenching towards lighter nuclei should rather be interpreted as a sign of additional MEC contributions.

6. In-medium vector meson scaling and magnetic electron scattering form factors The concept of a replacement of the nucleon mass mN by an effective mass m~q when imbedded in a nuclear environment with a certain density has been embodied in nuclear theory in numerous ways. As an example, Brown and Rho have pointed out the necessity of an enhancement of the p-meson exchange tensor interaction in the nuclear medium [ 5]. Since this modification is analogous to that of isovector transverse electron scattering form factors, magnetic transitions can be expected to be modified appreciably by a reduction of the tensor part of the nucleon-nucleon interaction [5,63]. Such effects were studied e.g. by Lallena [64] for the form factors of low-lying 2 - and 4 - transitions in 48Ca. His calculations were carried out in the framework of RPA using the Jiilich-Stony Brook residual interaction [65] incorporating a variable p-exchange strength Vres = C o ( g o 0-1 • 0 -2 + g~)0-1 . 0-27.1 . 7.2) + Vzr + e V p ( e ) ,

(10)

where

\ m*oJ The parameter e is a measure for the p-meson coupling strength, and for e = 1 the original interaction of Ref. [65] is attained. For simplicity, an explicit density dependence of m'pimp was neglected. The strength parameters go and g~ of the interaction were fixed to reproduce the energies and transition strengths of low-lying states in 2°8pb [66]. During the first experiments with the new 180 ° system described in the previous sections a short exploratory study (with the main emphasis on the background behaviour) of the 48Ca(e,e') reaction was already performed. The data taken at E0 = 50 MeV are depicted in Fig. 9. The spectrum is dominated by the famous M1 transition to the 10.23 MeV state which has served as a prime example for investigations of the different processes contributing to the quenching of magnetic dipole strength [ 16]. At 6.89 MeV (marked by an arrow) a transition to a known j~r = 2 - state is visible. The extracted form factor point is shown in the left part of Fig. 10 together with experimental results from Ref. [67] obtained at higher momentum transfers. The calculations of Ref. [64] with e in Eq. (10) varying at 1, 1.2, 1.6 and 2 are shown as solid, dashed, dotted and dashed-dotted lines, respectively. Clearly, the data exclude values e > 1.2. It is pointed out in Ref. [64] that this result stands in contradiction with e values extracted from other magnetic transitions in 48Ca. No consistent description can be obtained by a modification of the p-meson mass alone.

C. Lffttge et al./Nuclear Physics A 606 (1996) 183-200

196

I

15

'

'

'

I

'

'

I

'

'

'

I

'

48Ccl(e,e') " " , 10

5

Eo = 50

v

0

=

MeV

180 °

_

E-I o

5

(..)

I

I

I

,

n

i

8

1

q

I

L

I

10 Excifefion

L

I

I

I

12 Energy

t

,

14

(MeV)

Fig. 9. Spectrum of the 48Ca(e,e ~) reaction at Eu = 50 MeV measured with the 180° system• The arrow indicates the M2 transition to the level at Ex = 6.89 MeV discussed in the text.

10 -4 i

I

I

48Cc

I

10-4

I

I

Ex = 6.89 MeV

i

I

I

48C( ]

J" = 2-

. ,-..

,'

,,

",

,,' / , ,/"

'

10-5

-

',

,\

.

\

/ I

10-s

,'

',\,

J

"

I

I

I

Ex = 6.89 MeV

J" = 210-s

I

,

u_~

.

/~"

,,

10

/

-,',

~'

\',

~,~ .'

...

'

10-7

10 -s

10 -8

0.0

0.5

1.0 1.5 2.0 q°~,f (fm -r)

2.5

3.0

0.0

,

0.5

1.0

I

,

i

1.5 2.0 q . , (fro -1)

1

2.5

3.0

Fig. 10. Transverse form factor of the M2 transition to the Ex = 6.89 MeV, j r = 2 - state in 48Ca. The data at qeff > 1 fm - l (triangles) are fiom Ref. 167]. The curves are RPA calculations [64] using the residual interaction of Ref. [65] modified to allow for a reduction of mp (l.h.s.) or a simultaneous scaling of mp and f~ (r.h.s.) according to Ref. [6]. The solid, dashed, dotted and dashed-dotted form factors are obtained with coupling strength reduction factors I, 1.2, 1.6 and 2, respectively.

C. Liittge et al./Nuclear Physics A 606 (1996) 183-200

197

Thus, as a next step, one can consider a simultaneous scaling of the pion coupling constant f~,. A 'universal scaling' law for the effective nucleon (ms) and meson (m,,, m o, mo~) masses in the nuclear medium mN ~

m~

mN

m~

~

mp ~

mo~ "~

me

m~o

(12) f~r

was proposed by Brown and Rho [6]. It can be established starting from restoration of chiral symmetry at high baryon densities taking into account the scaling properties of QCD and provides e.g. a link between the mean field nuclear matter theory and a chiral perturbation description of kaon condensed matter [ 68]. While this concept is not entirely without problems [69], it provides nevertheless a working base which simultaneously accounts for the in-medium enhancement of the spin-orbit interaction [70-72] and the reduction of the tensor piece. The residual interaction used in Ref. [64] was modified to permit a simultaneous scaling of m o and f~r Wres = C o ( g o 0-1 • 0 -2 --}- g ; 0 - 1 . 0-27.1 . 7.2) _1_ l_WTrq_ eVp(~.). E

(13)

The r.h.s, of Fig. 10 presents the form factor of the 6.89 MeV transition in comparison to the calculations for different e using the refined interaction of Eq. (13). Here, the data at higher q allow for e = 1, 1.2 or 1.6, but the first maximum at low q is very sensitive to the assumed e value. While the result of our short exploratory run might not yet be statistically significant to distinguish between the three calculations, a careful mapping of the form factor for q -~ 0.5 - 1 fm -1 should solve the matter. Indeed, a full investigation of 48Ca in this momentum transfer range with the 180 ° system is planned for the near future.

7. Outlook We have discussed for a few selected examples how experimentally precisely determined low-energy nuclear structure information on the magnetic dipole and quadrupole response of nuclei may give insight into diverse fields such as the dynamics of stellar collapse and nucleosynthesis during the shock wave of a supernova, modifications of the vector meson interaction in the nuclear medium and effects of pionic currents in complex nuclei. A new 180 ° electron scattering system with unprecedented properties has been introduced which will serve as a 'work horse' for further investigations of M1 and M2 strengths in nuclei and their relation to basic nuclear physics problems (not to forget M3 transitions, almost a 'blind spot' in the nuclear structure landscape [73]). The future experimental program at the 180 ° system forms part of an international effort by the EUROSUPERNOVA collaboration including groups from U Bari/TH Darmstadt/U Gent/KVI Groningen/U Madrid/U Milano/U Mtinster which aims at an experimental determination of magnetic properties of nuclei relevant to the astrophysical

198

C. Liittge et al./Nuclear Physics A 606 (1996) 183-200

p r o b l e m s raised in Section 2. O n e o f the goals of the collaboration is the construction o f a highly efficient p o l a r i m e t e r for proton scattering experiments at K V I G r o n i n g e n p e r m i t t i n g angles close to zero degree. The c o m b i n a t i o n o f m e d i u m - e n e r g y polarized proton scattering at small m o m e n t u m transfer and 180 ° electron scattering will p r o v i d e a unique tool to unravel the l o w - m u l t i p o l a r i t y s p i n - i s o s p i n response in nuclei.

Acknowledgements We are indebted to H.-D. Gr~if and the S - D A L I N A C accelerator crew for p r o v i d i n g excellent electron beams and to B. R e i t z for his help in the data analysis. Discussions with J. W a m b a c h are gratefully acknowledged. This w o r k was supported by the B M B F under contract 06 D A 665 1 and by the E C H u m a n Capital and M o b i l i t y p r o g r a m C H R X CT94-0562. O n e o f us ( A . R . ) is very grateful for the inspiration and guidance, the support and w a r m friendship o f Gerry B r o w n experienced in g o o d and bad times ever since we first met at the f a m o u s 1965 Varenna S u m m e r School on " M a n y - B o d y Description o f Nuclear Structure and Reactions".

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