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            2                      PHYSICAL REVIEW LETTERS                                                    12 J A N U A R Y 1976

  'M. A . Locchi and P . Picchi, Nuovo Cimento 57, 803                 E. Rcid, G. J. Stephenson, J r . , and M. K. Baner-
(1968); A. Reitan, Nucl. Phys. E,     387 (1974).             jee, Phys. Rev. C 5,287 (1972).
  3 ~ R. Gibbs, Phys. Rev. C 3, 1127 (1971), and 5,
          .                                                      '.
                                                                'J LI. JIcKinley, Rev. AIod. Phys.         s, 788 (1963);
775 (1972).                                                   L. D. Roper, R. LI. Wright, and B. T. Feld, Phys. Rev.
  4 ~ R. Gibbs, J. C. Jaclrson, and W. B. Kaufmann,
           .                                                  138, B190 (1965); J . R . C a r t e r , D. V. Bugg, and A. A.
Phys. Rev. C 9, 1340 (1974).                                  C a r t e r , Tuucl. Phys. E, 378 (1973); D. Dodder, pri-
  5 ~ L. Foldy and J . D. Waleclra, Ann. Phys. (N.Y.) 54,
        .                                                     vate communication.
447 (1969); R. H. Landau and F. Tabaldn, Phys. Rev.             "A group at the University of Colorado has done an
D 5,2746 (1972); W. R. Gibbs, Phys. Rev. C i0, 2166           independent estiniate f o r 13C and obtain r e s u l t s s i m i l a r
(1974); J. T. Londergan, K. W. McVoy, and E. J. Moniz,        to ours. R. C. Anderson, J . J. Kraushaar, E . Rost,
Ann. Phys. (N.Y.) 86, 147 (1974).                                       .
                                                              and D. A Sparrow, private communication.
  6 ~ Shamai ef al., preceding Letter [Phgs. Rev. Lett.
        .                                                       "A. I. Yavin, R. A. Hoffsvvell, L. H. Jones, and T . M.
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36,                                                           Noweir, Phys. Rev. Lett. 23, 1049 (1966); J . Alster,
  7 ~ N. Boyarkina, Izv. Alrad. Nauk SSSR, Ser. Fiz.
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28, 337 (1964) [Bull. Acad. Sci. USSR, Phys. Ser. 28,         nloinester, Pliys. Rev. Lett. 28, 313 (1972); J. S. Lilley,
255 (1964)l.                                                  D. H. Fitzgerald, C. H. Poppe, S. M. Grimes, and
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      Possibility of Detecting Density Isomers         iil   High-Density Nuclear Mach Shock Waves*

                Hofmann, Horst Stöcker, Ulrich Heinz, Werner Scheid, and Walter Greiner
         Institut für Theoretische Physik der Lrniversität Frank&& anz Main, FrankjWt a m Main, Gemzany
                                           (Received 29 September 1975)

              Up to now no experimentally feasible method f o r detecting abnormal nuclear states has
            been known. We propose to observe them in high-energy heavy-ion collisions through the
            disappearance of, o r irregularities in, high-density nuclear Mach shocli phenomena.

    Even though nuclear density isomers were sug-           minimum and particularly the binding energy
gested recently by several a ~ t h o r s , ' -there has
                                                  ~         M0c2- \V2 of abnormal nuclear matter may shift
been up to now no known experimentally feasible             up o r down by a few hundred               Moreover,
way for their detection. We suggest here a rath-            the compression eilergy of the i s o m e r , which i s
e r simple and unique method for their observa-             determined by the cornpression constant K, = 9pZZ
tion, which i s based on high-density nuclear               x d 2 IV/dpZ2of the second minimum, may drasti-
Mach shock (HDNMS) waves and head shock waves
occurring during the interpenetration of high-en-
ergy heavy i ~ n s . = Indeed, the recent experi-
                                                            cally deviate from that of the ground state @,
                                                              300 MeV)8 and lead to very high sound velocities
                                                            in abnormal nuclear matter c,/c = (ap/ae)lI2 at
ments of Baurngardt e t ~ 1 could be consistently
                                         . ~                constant entropy, where e = LVp i s the energy den-
interpreted with the shock-wave concept. In par-            sity and p = p2 8W / a p i s the pressure. Requiring
ticular, these experiments lead to the conclusion           the conservation of fluu of baryons, energy, and
that the observed Mach angles cailnot be explained          inomentum across the shock front one gets the
with simple sound waves of low amplitudeg close             relativistic Rankine-Hugoniot (RRH) equation
to nuclear equilibrium density p o but that HDNMS
waves a r e necessary for which the actual density
p / p o i s approximately 3-6. At these densities
isomeric o r abnormal nuclear states nlay e ~ i s t l - ~
                                                            which uniquely connects the specific enthalpies
wliich will affect the properties of the nuclear
                                                            i = Wp +P and i, =It7,p, (P,= O), the pressure P ,
system. The situation can schematically be r e -
                                                            and the densities p and po oll the two sides of the
presented by the compression-energy functional
                                                            shock front. The index Zero denotes the unshocked
W c ( p ) [ ~ i g l(a)]. Its f i r s t minimum i s associ-
                                                            nuclear matter. For the energy per baryon W ( p ,
ated with the nuclear ground state of binding en-
                                                            T ) in compressed nuclear matter we made the
ergy M0c2- W o = 1 6 MeV, aild its second mini-
                                                            following Ansatz:
mum, separated by a b a r r i e r froin the f i r s t olle,
represents tlle density isomer. This secondary                    M7(p,T)=iVI0c2+  W,(p)+R7,(p,T),              (2)
     36,   2
VOLUME NUMBER                              P H Y S I C A L REVIEW LETTERS                                      12 JANUARY 1976

                                                                       tion (1)connects the temperature with the density,
                                                                       i.e., T = T(p). Hence we obtain within the shock
                                                                       wave W,( p , T(p))= W,(p) from the solution of the
                                                                       quadratic equatioii

                                                                       where a = a , + l ,


                                                                       with W,=Moc2- 16.456 MeV. W T ( p ) depicted
                                                                       in Fig. l ( c ) . In the ascending part of the ground-
                                                                       state niinimum where the p r e s s u r e p increases,
                                                                       W, ( i )behaves as known for normal nuclear mat-
                                                                       ter'; i.e., W,(p) i s a monotonically increasing
                                                                       function of $0, s o that the HDNMS wave will propa-
                                                                       gate through the nucleus and eject tlie shock par-
                                                                       ticles at the surface. This i s also reflected in
   FIG. 1. (a) Various schematic energy functionals                    the behavior of the shock velocity given by
~.{l(p, = 0). The f i r s t minimum a t the nuclear ground-
state density p o and secondary mininla of possible den-
sity i s o m e r s a t p, a r e separated by a b a r r i e r a t pl.
(b) The p r e s s u r e P@) in the compression region. It
vanishes a t p l , becomes negative, and again reaches                 and shown in Fig. l(d). In the region just men-
positive values a t p,. ( C ) Calculated wC(p)and fl/,(p)                                >
                                                                       tioned, V ,/C > c,/c which implies a HDNMS wave,
with Moc2 W O - 16.456 MeV at po= 0.17 fm-3, Ko = 300
                                                                       but at a certain density 5,v,/c shows a maxi-
MeV, and M ~ C '- W 2 = 15 MeV a t p 2 = 5p0. In the region
of negative p r e s s u r e , i .e ., between the maximum of           mum. As the W,@) b a r r i e r maximum i s ap-
                                                                       proached the p r e s s u r e p goes to 0 (because aI.If/
W, (p) a t p, and the secondary minimum a t p 2 , the RRH
equation i d no longer valid. The shock phenomena
breali down, which i s indicated by the two dashed lines
                                                                       ap 0). Therefore v,(Q)/c is decreasing, which
                                                                       means that the shock phenomena vanish. Simulta-
a t p , and p 2 . (d) The shock velocity v,(p) begins a t po           neously W,@) goes to 0 because of the i s o l ~ e r i c
with the sound velocity C,= ( K / ~ M ~ ) ' = 0 . 1 9 ~
proaches asymptotically (p/po W ) the velocity of
light C .
                                                            and ap-    cooling (the phase transition to the isomer ex-
                                                                       tracts internal energy). At even higher deiisities
                                                                        @ , s p sp,) the RRH equation i s no longer valid.
                                                                          This behavior indicates the phase t ~ a n s i t i o nof
where i1 , c 2 s 938.9 MeV i s the r e s t energy p e r
       l                                                               nuclear matter. Behiiid the potential b a r r i e r be-
nucleon, W,(p) i s the above mentioned compres-                        tween ground and isomeric states the p r e s s u r e
sion energy per nucleon at Zero temperature, for                       becomes even negative, which means that the
which we use the power expansion                                       compression Zone collapses into a new (abnor-
                                                                       mal) state which cools the hot ordinary matter.
                                                                       This accelerates the change of nuclear matter.
and Tlr,(p,T) is the thermal energy per nucleon.                       This effect i s similar to the condensation of a
The coefficients A -E fix the b a r r i e r height, iso-               gas into a fluid (state of higher o r d e r ) where the
meric density, and compressibility of the sche-                        van d e r Waals equation becomes invalid. To
matic model [Fig. l ( a ) ] . The pressure p in the                    s t r e s s this point we draw a p -V diagram for T = 0
compression Zone i s                                                   and for the variable T in the shocked matter
                                                                       which resembles to some extent that f o r the vail
                                                                       d e r Waals gas (Fig. 2). F o r densities higher than
                                                                       the isomeric ground-state density ,o„ the shock
                                                                       phenomenon should develop again. We assume
where p,=p28Wc/8p and CY = for ideal and F e r m i                     tliat the strongly compressed head shock moves
gases.' It i s shown in Fig. l(b). The RRH equa-                       rather friction-free through the normal nuclear
     36,    2                     PHYSICAL REVIEW LETTERS                                             12 J A N U A R Y 1976

                                                             FIG. 3. The Mach angle q ( E ) a s a function of the pro-
                                                           jectile energy (per nucleon, AT). The presently available
                                                           experimental r e s u l t s (Ref. 8) a r e indicated. The conse-
                                                           quence of a possible density isomer will affect the Mach
                                                           angles a s schenlatically indicated by the dashed curve.

                                                           mum value remarkably smaller than a r c cos(c,/
  FIG. 2. Pressure-volume (p-V) diagranl (forV=po/p)       C)=  80") because of the velocity of light a s an up-
of a qualitative comparison of dense nuclear m a t t e r   per liinit for ui,. q will again tend to Zero at
with an isomeric phase. It obviously reseinbles to         very high projectile energies (ui„/c- 1) because
some extent that of the van der Waals g a s , which also   @„,/C    i s a monotically increasing function of p
becomes invalid at the condensation point. Dashed          and also tends to 1 for p > 1 [Fig. l(d)].
curve: isothermal @-V diagram for W, = 0 (temperature        If a density isomer exists, this behavior will
T = 0 ; solid curve: $-V diagram calculated with the
                                                           be drasticaily changed: The Mach shock velocity
temperature dependence T(p) obtained by RRH equation.
                                                           decreases to Zero for a certain density region
                                                           [Fig. l ( d ) l , s o that the observable Mach angle
inatter with v -- Y ion. This kind of superfluidity        will reach 90". Then the Mach angle should
can happen via pion condensation, for which T' -           abruptly vanish in the energy interval where p,
71.- layers with-depending     on the proton-neutron       G p G p z and suddenly for p >p, reappear again at
ratio-autoionizing    T - cull OCCUF.  The T' layer        90" to follow the above mentioned trend to Zero
is tiglitly bound to the highly compressed core of         degrees (Fig. 3). This can serve as a unique sig-
the projectile, which s o stabilizes itself. We            nature for density isoiners o r abnormal behavior
then expect, because of the reaction ' +n -p,
                                         n                 of nuclear matter. It i s interesting to notice
proton-rich (neutron-poor) nuclei to dominate tlie         that the presently available experiinental data10
fragmentation products and an excess of f r e e n -        show a decrease of the Mach shock velocity from
over T * .                                                 0.87 to 2.1 GeV/nucleon with a nlaximim a t 0.87
    Now, f r o n ~ measureinent of the Mach angle
                 the                                       GeV/nucleon; See the followiilg table:
cp oiie can derive the Mach shock velocity, z',:~,              Ekinlab                   qexp    V ~ j = v i o n cosq
via the relation8                                            (GeT'/nucleon)       C      (deg)      C        c         exp

                                                                  0.25           0.61     35              0.50
For ordinary nuclear inatter one can expect qual-                 0.87           0.87     50              0.56
itatively the following results: At low projectile                2.1            0.95     65              0.40
velocities (energies) the Mach angle will be small         This i s perhaps a first indication for some spe-
and increase with projectile energy. It will not           cial sti-ucture of L V ( p , T ) , i.e., abnormal behavior
tend to 90' with asyinptotically high projectile en-       of nuclear matter. Nevertheless to definitely
ergies, as one would expect according to nonrel-           prove or disprove the existence of density iso-
ativistic gas dynanlics, but should have a maxi-           m e r s we suggest repeating the HDNMS-wave ex-
            2                                     P H Y S I C A L REVIE\V LETTERS                                                        12 JANUARY 1976

p e r i n l e n t by bonlbarding, e.g., lo7Ag or '08Pb w i t h                      5 ~ K . I<erman, in Proceedings of the Second High En-
160 n s m a l l s t e p s of incident e n e r g y (about 50
       i                                                                          ergy Heavy Ion Summer Study , Berkeley , California,
MeV/nucleon) f r o m 0.05 to 2.1 ~ e c / n u c l e o n (if                        July 1974, edited by L. Schroeder, Lawrence Berlceley
                                                                                  Laboratory Report No. LBL 3675 (unpublished).
p o s s i b l e h i g h e r ) and s y s t e m a t i c a l l y m e a s u r i n g
                                                                                    'W. Scheid, H. Miiller, and W. Greiner, Phys. Rev.
t h e s h o c k angles." T h e s e m e a s u r e m e n t s w i l l e n -          Lett,      741 i1974).
a b l e u s t o e x p l o r e t h e e n e r g y function W ( p , T ) ,                'J. Hofmann, W. Scheid, and W. Greiner, "Thermal
its eventual i s o m e r s t r u c t u r e s , arid also t h e t e m -            Excitation of Nucleons in Nuclear Shock Waves" (to be
p e r a t u r e b e h a v i o r of a highly c o m p r e s s e d n u c l e a r     published) .
g a s . S u c h e x p e r i m e n t s should p r e s e n t l y b e pos-               'H. G. Baumgardt, J. LT. Schott,   Sakamoto, E . Schop-
s i b l e without m a j o r difficulties.                                         p e r , H. Stöclier, J . Hofniann, W. Scheid, and W. Grei-
   W e thank P r o f e s s o r E. S c h o p p e r f o r many v a i -              n e r , Z . Phys. A 3, (1975).
                                                                                      'A. E . Glassgold, W. Hecltrotte, and K. M. Watson,
uable discussions.
                                                                                  Ann. Phys. (N.Y.) 6 , 1 (1959).
                                                                                    'OA recalibration of the data of Ref. 8 has shifted the
                                                                                  experimental Mach angles to somewhat larger values
                                                                                  a s shown in Table I ( E . Schopper, private communica-
  *Work supported by Bundesministerium für Forschung                              tion)  .
und Technologie and by Gesellschaft fiir Schwerionen-                               "~he     occurrence of transparency-as   postulated by
forschung.                                                                        M. I. Sobel, P. J . Siemens, J . P . Bondorf, and H. A.
  'A. R . Bodmer, Phys. Rev. D 4, 1601 (1971).                                    Bethe, to be published-can presently not be ruled out.
  2 ~ D . Lee and G. C. Wick, Phys. Rev. D 9, 2291
       .                                                                            "The strength of the density isomer may depend on
(1974).                                                                           the number of nucleons. This can be experimentally
  3 ~ D. Lee, Rev. Mod. Phys. g,
        .                          267 (1975).                                    found out by systematically choosing heavier projectile
  4 ~ D. Lee and M. Margulies, Phys. Rev. D 11,
       .                                          1591                            and target nuclei and repeating the excitation function
(1975).                                                                           of the RiIach angle.

                  Homogeneous Broadening of Optical Transitions in Organic Mixed Crystals

                                      H a r m e n d e V r i e s and Douwe A. W l e r s m a
Laboratory for Physical C h e m i s f r ~Einiversity of Groningen, Zemikelaan, Paddepoel, Groningen, The Netherlands
                                                  (Received 21 October 1975)

                  We have used the phenomenon of laser-induced molecular photodissociation to determine
                the homogeneous linewidth at 2 K of the origin (zero-phonon line) and a vibronic transition
                in the mixed-crystal absorption spectrum of dimethyl s-tetrazine in durene. From the
                measured 55-MHz (upper limit) homogeneous width of the origin we conclude that in the vi-
                brationless excited state coherence persists at least during the 6-nsec lifetime. The 29-
                GHz homogeneous vibronic linewidtl~i s ascribed to vibrational relaxation.

    It i s s t i l l m a i n l y a m a t t e r of s p e c u l a t i o n a s t o   t h e homogeneous linewidth of a v i b r o n i c t r a n s i -
what extent t h e linewidths i n t h e l o w - t e m p e r a t u r e              t i o n i n t h e s p e c t r u m of p e n t a c e n e embedded in a
" s h a r p " line a b s o r p t i o n and e m i s s i o n s p e c t r a of       p - t e r p h e n y l h o s t c r y s t a l . T h e u n d e r l y i n g homo-
o r g a n i c mixed c r y s t a l s are inhomogeneously                           geneous linewidth of t h e 3 - c m - l - w i d e v i b r o n i c
broadened.' In o r g a n i c c r y s t a l s t h e only r e p o r t               t r a n s i t i o n w a s found t o b e 0.026 c m - ' and t h e a u -
of a homogeneous linewidth of a v i b r a t i o n l e s s                         t h o r s concluded f r o m t h i s t h a t v i b r a t i o n a l r e l a x a -
t r a n s i t i o n Comes f r o m H o c h s t r a s s e r and Li2 who             t i o n in t h i s s t a t e w a s as slow as 200 p s e c . T h e
showed t h a t t h e o r i g i n (zero-phonon line) of t h e                      q u e s t i o n of Course arises w h e t h e r s u c h a slow
l o w e s t s i n g l e t s t a t e in a z u l e n e a s guest in naph-           vibrational relaxation p r o c e s s i s typical f o r o r -
t h a l e n e w a s m a i n l y homogeneously broadened.                          g a n i c s at low t e m p e r a t u r e o r t h a t a g a i n a n e x c e p -
In t h i s exceptional c a s e t h e r e i s a n e x t r e m e l y                t i o n a l c a s e w a s studied. W e h a v e d e s i g n e d a n op-
f a s t (2.6-psec) nonradiative e l e c t r o n i c r e l a x a t i o n           t i c a l "hole-burning" e x p e r i m e n t t h a t not only a n -
p r o c e s s t h a t i s r e s p o n s i b l e f o r t h e o b s e r v e d 2-    s w e r s t h i s l a t t e r question, but a l s o p e r m i t s u s ,
c m - ' o r i g i n linewidth. R e c e n t l y M a r c h e t t i , Mc-            f o r the f i r s t time, to measure directly the under-
Colgin, a n d E b e r 1 9 r e p o r t e d a m e a s u r e m e n t of              lying homogeneous linewidth of a zero-phonon