PHYSICAL REVIEW C, VOLUME 61, 014301

Effect of neutron excess onD excitations in exotic nuclei

Mahmoud A. Hasan,1,2 James P. Vary,2,3 and T.-S. H. Lee41Applied Science University, Amman, Jordan

2International Institute of Theoretical and Applied Physics, Ames, Iowa 500113Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011

4Physics Division, Argonne National Laboratory, Argonne, Illinois 60439~Received 1 June 1999; published 23 November 1999!

The effects of neutron excess on the formation ofD(3,3) resonance states in exotic nuclei at equilibrium andunder large amplitude compression have been investigated within the radial constraint spherical Hartree-Fockmethod. An effective Hamiltonian has been used which includes theD degree of freedom explicitly. Resultsare presented for28O, 60Ca, and70Ca in a model space of seven major oscillator shells and eightD orbitals.The results show that the formation of theD ’s depends strongly on the amount of neutron excess in the nuclearsystem. In contrast to previous work where we found noD ’s in 16O and40Ca at equilibrium, these results showthat a significant amount ofD ’s exists at equilibrium in exotic isotopes. In addition, as the nucleus is com-pressed to a density of 2.5 times the ordinary nuclear density, the percentage of theD ’s rises to 3%, 5%, and7% of the total number of all baryons in28O, 60Ca, and70Ca, respectively. This suggests a parametrization forthe percentage of theD ’s created at 2.5 times the normal density of the form 0.25(N2Z)%. The results areconsistent with the theoretical prediction of the formation ofD matter in neutron-rich matter at highcompression.

PACS number~s!: 21.10.Pc, 21.60.Jz, 21.65.1f, 24.30.Gd

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I. INTRODUCTION

With the advent of high precision experiments at intermdiate and high energies using a variety of probes, the cobution of baryon resonances to the structure of nuclei in thground state and under compression becomes a major exmental and theoretical question@1,2#. For example, somerelativistic heavy ion collision data@3,4# show that as muchas 10% of the nuclear system can be excited intoD reso-nances. Nucleons are no longer adequately treated aementary or structureless particles, and the internal dynamof nucleons has to be taken into consideration. One metthat incorporates the dynamics associated with the strucof the nucleons in the nuclear system is to consider thecitations of the nucleon intoD isobars.

In this paper we investigate the effect of neutron excon the formation of theD ’s in 28O, 60Ca, and70Ca at equi-librium and under radial compression. We investigate athe role of theD on the ground state properties of thenuclei. The calculations have been performed using a sphcal mean field method@constrained spherical Hartree-Foc~CSHF!# with a model space of seven major oscillator sheand a realistic effective Hamiltonian@5# Heff which containstheNN, N-D, andD-D interactions. The complete effectivbaryon-baryon interaction has been evaluated usingBruecknerG-matrix @6# method, an improvement that whave adopted in Ref.@7#. We present results for energies amatter densities for nucleons andD ’s for 28O, 60Ca, and70Ca at equilibrium and under compression.

In our previous works@7,8# we have investigated the rolof D ’s in several closed shell and closed subshell nuclei nthe valley of b stability, namely, 16O, 40Ca, 56Ni, 90Zr,100Sn, and 132Sn. At equilibrium, we found that nucleonand D ’s mix only in nuclei which have an excess of netrons, that is, in90Zr and 132Sn, but not in the other nucle

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By applying a static radial load, the population of theDorbitals sharply increases with increasing load. Our goal his to investigate the effect of the neutron excess on theDpresence in more neutron-rich exotic nuclei at equilibriuand under compression.

We are well aware of the fact that these nuclei lieaway from the nuclear valley of stability. However, we aticipate that, by investigating the role ofD ’s in these exoticnuclei, we can provide insights into intermediate and henergy heavy ion collision processes, where nuclei penetinto each other and reach densities 2–3 times higher tnormal. Furthermore, at intermediate impact parameters,interaction regions comprise a neutron-rich system whatomic, neutron, and proton numbers could be in the rangthe systems we investigate here.

Furthermore, there are recent experimental and theoreinvestigations of some of these systems@9,10#. Projectilefragmentation experiments have shown particle instabifor 28O @9#. A recent mean field analysis has found that70Calies on the border of two-neutron stability@10#.

One may also speculate that lower energy heavy ionlisions, above the Coulomb barrier, could produce siminteracting regions where allowance forD ’s in the initial andintermediate states could provide a mechanism for ‘‘sthreshold’’ pion production processes.

This paper is organized as follows: In Sec. II we presthe effective HamiltonianHeff and the model space usedthis calculation. In Sec. III we summarize our procedure astrategy. Results and discussion are presented in Sec. IV

II. EFFECTIVE NO-CORE HAMILTONIAN H eff

AND MODEL SPACE

For a nuclear system ofA baryons~nucleons of massm,spin s51/2, isospint51/2, andD baryons of massM, spin

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MAHMOUD A. HASAN, JAMES P. VARY, AND T.-S. H. LEE PHYSICAL REVIEW C61 014301

s53/2, isospint53/2) the intrinsic mass operator can bwritten as

H5T2Tc.m.1VBB81VC , ~1!

whereT is the single-particle~sp! mass and kinetic energterm, Tc.m. is the center-of-mass kinetic energy,VBB8 is thestrong two-baryon interaction operator given by

VBB85VNN↔NN1VNN↔ND1VND↔ND1VND↔DN

1VND↔DD1VNN↔DD1VDD↔DD, ~2!

and VC is the two-particle Coulomb interaction acting btween charged baryons. We define

Trel5T2Tc.m., ~3!

with

T5(i 51

A F S pi2

2m1mDL i

1/21S pi2

2M1M DL i

3/2G ~4!

and

Tc.m.5Pc.m.

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2m, ~5!

wherepi is the sp momentum operator, andLt is a sp iso-spin projection operator:

Ltut8&5dtt8ut8&, ~6!

L1/21L3/251. ~7!

The intrinsic mass operatorH can be written as

H5H1~one body!1H2~ two body!, ~8!

where

H15(i 51

A F pi2

2M S m2M

m D1~M2m!GL i3/2 ~9!

and

H25Trel1VBB81VC , ~10!

where

@Trel~m!# i , j5~pi2pj !

2

2mA~11!

is the relative kinetic energy operator. In this manipulatiowe eliminate the center-of-mass kinetic energy in favorthe relative kinetic energy. In Eq.~5!, MA is the total mass ofthe nuclear system. In generalMA is state dependent, but wapproximateMA5Am and neglect binding energy effectsthe kinetic energy operator. The termH1 arises from themass difference between a nucleon andD and gives nonzero

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contribution when it acts on many-body states withD com-ponents. States withD components are said to comprise tD sector.

In principle, if one solves the Schro¨dinger equation in thefull infinite Hilbert space of all possibleN andD many-bodyconfigurations, then one gets the exact solution. Technicathis is not feasible beyond light nuclei of aboutA512 wherespecial procedures may be adopted. Therefore, we trunthe infinite Hilbert space and define an effective HamiltonHeff to be used in the truncated model space. In this w

VBB8 in Eq. ~10! becomesVeffBB8 and Eq.~10! reads

H2~ two body!5Trel~m!1VeffBB81VC . ~12!

By applying the variational principle, Hartree-Fock equtions for N and D orbitals can be derived to use with theffective Hamiltonian within the chosen model space. Copression is achieved by imposing a static load, i.e., a rar 2 constraint. For details see Ref.@8#.

The matrix elements of the effective baryon-baryon intaction have been calculated using the BruecknerG-matrixmethod. The effectiveN-N interaction is the sum of theBruecknerG matrix and the lowest order folded diagra@11# ~second order inG) acting between pairs of nucleonsa no-core model space@11#. We adopt the Nijmegen~Nijm.II ! potential@12# for the N-N interaction.

The effective interactions associated with theD ’s areevaluated according to the method developed in Ref.@13#.The G-matrix elements are generated from a coupled chnelsNN% ND % pNN model@14–16# which was constrainedby the data of both theN-N elastic scattering and theNN% ND % pNN reaction up to 1 GeV. The procedure and stregy which we follow here are the same of Refs.@8,11,17#.

We view the constructed effective Hamiltonian to consof four sectors with matrix elements as follows.

~1! N-N sector:

^Trel~m!&1^VeffNN&1^VC

NN&.

~2! N-D sector:

^VeffND&1^VC

ND&.

~3! D-N sector:

^VeffDN&1^VC

DN&.

~4! D-D sector:

^H1~one body!&1^Trel~m!&1^VeffDD&1^VC

DD&.

For theN-N sector we include the lowest six major ocillator shells, i.e., 21 nucleon orbitals with fixedn,l andtotal angular momentumj. For theD we use the followingeight-oscillator orbitals: 0S3/2, 0P1/2, 0P3/2, 0P5/2, 1S3/2,1P1/2, 1P3/2, and 1P5/2.

In earlier work@8# we found that the higher the degreecompression we wish to obtain, the larger the model spwe need to include in order to achieve model space indepdent results. Since our goal is to examine theD components

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EFFECT OF NEUTRON EXCESS OND EXCITATIONS . . . PHYSICAL REVIEW C 61 014301

under large compression, we add a phenomenological exsion of the seventh major oscillator shell~with l .5 ex-cluded! to the nuclear model space. Therefore, the total nuber of baryon orbitals of specified (nls j) is 34 ~i.e., 26nucleon orbitals plus eightD orbitals!.

Matrix elements involving nucleons in the seventh share given by a simple sp Hamiltonian

h5t1U~r !1UC , ~13!

where t is the sp kinetic energy,U(r ) is the Woods-Saxonpotential given by

U~r !5U0

11expS r 2R

a D , ~14!

whereU05260 MeV, a50.6 fm, andR51.1A1/3 fm, andUC is the Coulomb potential of a uniform charge sphereradiusR. This completes the picture of the effective Hamtonian and model space which we use in these calculatio

III. CALCULATIONAL PROCEDURE AND STRATEGY

Here, we follow our established procedure of Re@8,11,17# by adjusting the two-body matrix elements in thN-N sector to fit the Hartree-Fock energy (EHF) and the rootmean square radius (r rms) to the experimental nuclear binding energy and radius, respectively. Since these nucleinot directly accessible in the laboratory, we explore altertives for estimating their binding energy and radii.

First, we estimate the nuclear binding energy froWeiszacker-Sachs semiempirical mass formula@18# given by

EBE5avA2asA2/32aCZ~Z21!A21/3

2asym~A22Z!A211d, ~15!

where d5apA23/4 for even N and Z, av515.5 MeV, as516.8 MeV, aC50.72 MeV, asym523 MeV, and ap534 MeV. This produces total binding energies of~150,450, 440 MeV! for (28O, 60Ca, 70Ca), respectively. Alternatively, we may adopt the parametrization of Mo¨ller, Nix, andKratz @19# to obtain~166, 458, 466 MeV!, respectively, forthese same nuclei. These binding energies are rather simwith the largest percentage difference occurring for28O. Weactually performed our study for both binding energies28O and found no qualitative difference in the results excfor an overall shift in the binding energy versus rms radiHence, for the purposes of this paper, we will present resfor the choices of binding energies~166, 450, 440 MeV! for(28O, 60Ca, 70Ca), respectively.

The nuclear mass radius is estimated from nucleartematics to ber 5r 0A1/3, with r 051.1 fm. However, theseexotic neutron-rich nuclei are expected to have a neuradius significantly larger than the proton radius. Perhathey could even develop a neutron halo. Thus, it is of sointerest to examine the resulting neutron and proton equrium radii separately. As expected, they are quite differ~see Table I!. Indeed, our calculated point proton charge ra

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~column 2 of Table I! are in good accord with phenomenological estimates~column 1 of Table I! of Aboussir et al.@20#. Examining the cube of the ratio of neutron to protoradii for 70Ca we observe that the neutron-to-proton volumratio is 2.2 while the ratio of neutrons to protons is 2Hence, we observe a very substantial outer layer of neutrin this system.

We introduce the parametersl t andlv to adjust the over-all strength of the matrix elements ofTrel and Veff , respec-tively. We obtain the fit for a given nucleus in a given modspace at equilibrium with theD channel omitted. For moredetails see Refs.@8,11,17#. We also scale the two-body matrix elements in theN-N sector~initially calculated with theoscillator energy\V514 MeV) to an optimal value\V8for each nucleus in each model space~for more details seeRef. @11#!.

Given three parametersl t , lv , and\V8 it is possible toobtain a fit forEHF andr rms. Nuclear binding energiesEg.s.,nuclear radii to which we fitEHF andr rms and resulting val-ues of the parametersl t , lv , and\V8 are given in Table II.We then apply the static load (r 2 constraint! to compress thenucleus. Finally, we activate theD channels, check the equlibrium solution now for the presence ofD ’s, and apply thestatic load again to compress the nucleus.

TABLE I. Values in fm for the equilibrium proton, neutron, anmass radii of the nuclei in this investigation. Parameters ofeffective Hamiltonian are adjusted to fit the quoted value of the rmass radius. Other radii result from the mean field evaluation.values labeled ‘‘ETFSI’’ correspond to the phenomenologicalsults of Ref.@20#. The rms radii for28O are virtually unchangedwhen theD ’s are included except the proton radius which decreaby 0.01 fm.

Nucleus r (ETFSI) r (proton) r (neutron) r (mass)

28O — 2.87 3.51 3.3460Ca 3.67 3.73 4.56 4.3070Ca 3.79a 3.71 4.81 4.53

aExtrapolated from the ETFSI systematics of the Ca isotopes.

TABLE II. Values of the nuclear ground state energy (Eg.s.) andradius~r! for 28O, 60Ca, and70Ca obtained from the fitting procedure. TheEg.s. fit values are within 1 MeV of the target valueswhile the calculatedr values agree with the parametrizationr5r 0A1/3, with r 051.1 fm. The oscillator energy\V8 and thestrength parametersl t and lv are used to adjustTrel and Veff

NN ,respectively, to fitEHF and r rms for each nucleus to the nucleaground state energyEg.s., and the nuclear radiusr rms. The N-Npotential used in these calculations is the Nijmegen~Nijm.II ! po-tential. The calculations are performed in a model space of semajor oscillator shells.

NucleusEg.s.

~MeV!r rms

~fm!\V8

~MeV! l t lv

28O 2165 3.34 6.80 0.970 1.19060Ca 2449 4.30 5.90 0.965~0.970!a 1.18170Ca 2439 4.53 6.08 0.980~1.00!a 1.148

aD channels are activated.

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MAHMOUD A. HASAN, JAMES P. VARY, AND T.-S. H. LEE PHYSICAL REVIEW C61 014301

FIG. 1. Constrained spherical Hartree-Fo~CSHF! energy vsr rms for 28O, 60Ca, and70Ca ina model space of seven major oscillator she( l .5 excluded! with D excitation restricted tothe eightD orbitals 0S3/2, 0P1/2, 0P3/2, 0P5/2,1S3/2, 1P1/2, 1P3/2, and 1P5/2. The solid~dashed! line corresponds toN1D ’s (N only!.

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Usually, if someD ’s are present in the equilibrium solution, we readjust the fitting parameters in order to insureoriginal starting point~same EHF and samer rms as withnucleons only active! before applying the static load with thD channels activated. For the nuclei in this investigation,found mixing between nucleons andD ’s at equilibrium. Weadjusted the value ofl t for 60Ca and70Ca to have the samEHF and r rms with and withoutD ’s ~see Table II!. For 28O,however, we kept the values of the fitting parameters wand withoutD ’s the same to exhibit the~small! effect of theD ’s on theEHF at equilibrium.

These calculations are performed in a no-core mospace containing a total of 34 baryon orbitals as descriabove. We allow for transitions from the 26 nucleon orbitto the eightD orbitals within the limits of CSHF. We workin a goodTz scheme where neutrons andD0 states are al-lowed to mix, as well as the protons with theD1 states. Thenumber of baryonic degrees of freedom for eachTz511/2,21/2 value is 174 single-particle states~142 nucleon statesand 32D-sp states! for an overall total of 348 sp states.

IV. RESULTS AND DISCUSSION

Results for28O are presented in Figs. 1–4, and results60Ca are displayed in Figs. 1 and 2, while results for70Ca aredisplayed in Figs. 1, 2, 4, and 5.

In Fig. 1 we display results forEHF vs point mass rmsradiusr rms for 28O, 60Ca, and70Ca. Dotted lines represenresults of calculations performed in the nucleon-only secwhile solid lines represent results obtained when theD ’s areadded in the eight orbitals specified above. It is worth mtioning here that, in the CSHF approximation, the nucleoand theD ’s may only mix in 0P1/2, 0P3/2, 1P1/2, and 1P3/2orbitals.

Even though we limit our discussion to the range of copression where the model space may be considered a reable one, we will shed some light on the region wherenuclear volume is reduced by 2/3 of its size at equilibriu

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Note that we define the volume at a given static load todefined by the rms radius via 4/3p r rms

3 .At equilibrium, there is increased binding by about 2

MeV, 3.5 MeV, and 20.0 MeV when theD ’s are includedover the results obtained with nucleons only~if the sameadjusting parameters are used forN-only andN1D ’s calcu-lations! for 28O, 60Ca, and70Ca, respectively. This is showin Fig. 1, only for 28O. For 60Ca and70Ca it was sufficient toadjust onlyl t when we added theD ’s to have the sameEHFand r rms for N1D ’s andN only.

For the sake of comparison we restrict our discussionthe specific situation where the reduction in the nuclear vume due to the load is about 22.5% compared to the nucvolume at equilibrium. At this compression, we find increased binding by about 3.5 MeV, 26 MeV, and 13 Mewhen theD ’s are included over the results obtained winucleons only, for 28O, 60Ca, and 70Ca, respectively.Viewed another way: it ‘‘costs’’ about 10 MeV~13.5 MeV!,30 MeV ~56 MeV!, and 27 MeV~40 MeV! of excitationenergy to achieve a 22.5% volume reduction in theN1D ’s(N-only! results for28O, 60Ca, and70Ca, respectively. Thismeans that, in general, the static compression modulusignificantly reduced by including theD ’s, and this reductionis the largest for60Ca and the smallest for28O. One mayalso infer that the inclusion ofD resonances induces a significant softening of the nuclear equation of state for laramplitude compression.

In Fig. 1, for 28O, we observe that if the reduction ivolume moves to 32%, the increased binding becomesMeV, which is about 6~20/3.5! times the increased bindinwhen the volume reduction is 22.5%. On the other hand,70Ca, if the reduction in volume moves to 26%, the icreased binding becomes 33 MeV, which is 2.5~33/13! timesthe increase in binding when the reduction is 22.5%. Tmeans that, when theD ’s are included in the nuclear systemthe 28O system appears more responsive to increasing cpression~as gauged by a fraction reduction in the volum!than 70Ca.

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EFFECT OF NEUTRON EXCESS OND EXCITATIONS . . . PHYSICAL REVIEW C 61 014301

FIG. 2. Number ofD ’s vs r rms under com-pression for 28O, 60Ca, and 70Ca. The modelspace is the one of Fig. 1. The dashed, dotted,solid lines correspond to the number ofD1, D0,andD11D0 formed which are equal for28O.

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Figure 2 displays the number ofD ’s created as a functionof r rms for the same range of compression for28O, 60Ca, and70Ca. At equilibrium~22.5% volume reduction! we find mix-ing between nucleons andD ’s for the three nuclei, where thnumber ofD ’s is 0.005 ~0.011!, 0.007 ~0.046!, and 0.034~0.058! of oneD for 28O, 60Ca, and70Ca, respectively. Thismeans that, out of the 10 MeV, 30 MeV, and 27 MeVexcitation energy used to obtain a volume reduction22.5%, 2 MeV, 12 MeV, and 7.2 MeV are needed to crethe additional rest mass of theD particles for28O, 60Ca, and70Ca, respectively. Therefore, about 20%, 40%, and 27%this excitation energy is utilized to create theD resonancesfor 28O, 60Ca, and70Ca, respectively. A corresponding increase in the interaction energy is therefore obtained to babout the stated reduction in overall energy. In other wocompressing these nuclei at low excitation energy appeabe an efficient mechanism to createD resonances in thessystems.

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We note in passing the significant isospin asymmetrythe D-resonance formation in these systems. At a volureduction of 22.5% the ratio ofD0:D1 is 1:1, 7:1, and 3:1 for28O, 60Ca, and70Ca, respectively.

We found that as we compress the nucleus to a densittwice the normal density~this corresponds to a radius o2.735 fm, 3.400 fm, and 3.58 fm for28O, 60Ca, and70Ca,respectively!, the number ofD ’s created sharply increasesabout 0.84, 3.2, and 4.4 for28O, 60Ca, and 70Ca, respec-tively. As a percentage, this means that 3%, 5%, and 7%all the baryons of the nuclear system are converted intoD ’s.One can conclude from this that, at approximately a fixreduction in the specific volume, the number ofD ’s formedis proportional to the excess of neutrons in the nucleussimple formula which gives this percentage is 1/4(N2Z)%, whereN andZ are the number of neutrons and prtons, respectively, in the nucleus.

We must mention again that the size of our model spac

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FIG. 3. Lowest eight CSHF zero-charge senergy levels vsr rms for 28O. The model spaceused is the one of Fig. 1. Solid~dashed! linesrepresent the results of calculations forN1D ’s(N only!.

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MAHMOUD A. HASAN, JAMES P. VARY, AND T.-S. H. LEE PHYSICAL REVIEW C61 014301

FIG. 4. Lowest eight CSHF zero-charge senergy levels vsr rms for 28O and 70Ca. Themodel space is the one of Fig. 1. Solid~dotted!lines represent the results of calculations forN1D ’s for 28O (70Ca).

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limited. Therefore, our results for high density is mospeculative. Clearly, in order to examine these results mcarefully, our next effort is to enlarge the size of our modspace. Enlarging the space allows for more compressiona more accurate quantitative prediction.

In Fig. 3 we display the lowest eight self-consistent zecharge sp energy levels as a function ofr rms for 28O. Theselevels are dominantly nucleons in character. The firstorbitals are occupied and accommodate the 20 zero-chbaryons.

In Fig. 4 we display the first eight neutral baryon orbitafor 28O ~solid lines! and 70Ca ~dashed lines! when theD ’sare included. The response of these single-particle statecompression exhibits similar trends. The less-bound orbimove up, as a function of decreasing radius, more quicthan the deeply bound orbitals. Note that only the lowestneutral baryon orbitals are occupied in28O while the lowest

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eight neutral baryon orbitals accommodate only 32 of theneutral baryons in70Ca.

It is clear that with compression, the orbits are brougdown by the contributions to the mean field attraction duemixing of nucleons andD ’s. The general trend exhibited inFigs. 3 and 4 is that the sp energies move up as the nucis compressed. Also, the ordering of the calculated spectfollows the expected ordering of the phenomenological shmodel @18,21#. With compression, the gaps between sheand the ordering of the sp orbits are preserved. Note thathigher orbits~orbits close to zero sp energy! are more sensi-tive to compression, which means that the surface is mresponsive to compression than the interior of the nucleu

The inclusion of theD ’s, as shown in Fig. 3, has a significant effect on reducing the compressibility of the nuclesystem. The trends are common to all three nuclei we invtigated, so we do not display all the results. To quantify

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FIG. 5. The eight zero-charge self-consistesp energy levels vsr rms for 70Ca that are domi-nantly D0 in character. The model space is thone of Fig. 1.

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EFFECT OF NEUTRON EXCESS OND EXCITATIONS . . . PHYSICAL REVIEW C 61 014301

different responses of these systems, we can take a fivolume fraction reduction and examine the behavior ofsp orbitals. Consider the slope of the zero-charge 0F7/2 or-bital at 22.5% nuclear volume reduction. WithD ’s includedthe slope for this orbital is (2110,2135,290) MeV/fm for28O, 60Ca ~not shown!, and 70Ca ~not shown!, respectively.The corresponding radii at which these slopes are evaluare ~3.075, 3.95, 4.16! fm. From these three results, no sytematic trend emerges. Thus, the flattening of the orbits wdecreasing radii at these compressions by the inclusion oD ’s would appear to be the single most dominant systemfeature.

In order to give a view of the sp behavior on a largenergy scale, Fig. 5 displays the eight dominantlyD0 orbitalsvs r rms for 70Ca. There is a gap of about 260 MeV~notshown! between the last neutron orbital and the firstD0 or-bital. The ordering of these orbitals proceeds from loweshighest as 0S3/2, 0P5/2, 0P3/2, 0P1/2, 1S3/2, 1P5/2, 1P3/2,and 1P1/2. There is a gap of about 45 MeV between then50 shell and then51 shell.

With compression the ordering of these orbitals andgap is preserved. Note that then51 orbitals are more sens

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tive to compression~as indicated by their slopes! than then50 orbitals. Also, note that the probability of mixing between nucleons andD ’s is higher forn50 orbitals than forn51 orbitals as indicated by the shifts between resultstained with and withoutD ’s.

The results presented herein already indicate that ccompression is an efficient mechanism for producingD reso-nances in exotic neutron-rich systems. For volume redtions up to about 30%, we expect the results already obtato be accurate predictions from the theory. To improve oability to make quantitative comparisons with experimeand to reach higher compressions and excitations, weinvestigate the excitation ofD ’s in larger model spaces anat finite temperature in future efforts.

ACKNOWLEDGMENTS

We acknowledge support for this work from U.S. DOGrant No. DE-FG02-87ER40371, U.S. DOE Contract NW-31-109-ENG-38, and National Science Foundation GrNos. INT-921507 and INT-9507430.

. J.

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@1# E. A. Pasyuk, C. L. Morris, J. L. Ullmann, J. D. Zumbro, LW. Kwok, J. L. Matthews, and Y. Tan, Acta Phys. Pol. B29,2335 ~1998!.

@2# C. L. Morris, J. D. Zumbro, J. A. McGill, S. J. Seestrom, R. MWhitten, C. M. Reidel, A. L. Williams, M. R. Braunstein, MD. Kohler, and B. J. Kriss, Phys. Lett. B419, 25 ~1998!.

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