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Isovector giant dipole and quadrupole resonances, and Direct+Semidirect photonucleon reactions. M. H. Urin (MEPhI, KVI)

Plan 1. 2. 3. 4. Aims Methods Results Summary

Collaborators: M.L. Gorelik (MEPhI) I.V. Safonov (MEPhI) B.A. Tulupov (INR RAN)

1


1. Aims · In the main, we attempt to describe in a semimicroscopic way the partial DSD and SD photonucleon reactions in the vicinity of the IVGDR and IVGQR in medium- and heavy-mass spherical nuclei. · Up to now only the phenomenological DSD model is used. The SD (p)-reactions via IVGDR> (the specific double GR) aren't described. · To reach the main aim, we check abilities of the approach and specify model parameters by description of photoabsorption in the vicinity of the IVGDR. Then the gross properties of the IVGDR multiplet, of the IVGQR and, that is most important, the DSD and SD photonucleon reactions are described without use of adjustable parameters. · Schematic representation of the IVGDR multiplet (separate page)
2


· The operators V ( x ) = V ( xa ) generating the excitations: a r (i ) (i ) (i ) ( + ) ( 3) ( - ) V ( x ) = V ( r )Y ( n ) , = , ,
L L LM

{

}

· DSD (n)-, (n)-, (p)-reactions via IVGDR< . Specific SD (p)-reactions via IVGDR> . Asymmetry (relatively 90º) of the (n)-reaction differential cross section is due to interference of the amplitudes of the DSD(1-)- and SD(2 )-reactions in the vicinity of the IVGQR.
+

3


2. Methods Semimicroscopic approach is based on the continuumRPA method and a phenomenological treatment of the spreading effect. Input quantities: a phenomenological mean field and the (i) momentum-independent Landau-Migdal p-h interaction bound by some selfconsistency conditions (for the problems under consideration the isospin selfconsistency is most important), the mean-field and interaction parameters are found from independent data; (ii) the energy- and radial-dependent smearing parameter directly introduced into the CRPA eqs. (in spirit of the optical model for the nucleonnucleus scattering); (iii) the "velocity" parameter, used to take effectively into account contribution of the isovector momentum-dependent forces in formation of the isovector (nonspin-flip) GRs.
4


2. Methods (continuation) Quantities calculated in the CRPA for a given probing operator V (x) (very schematically): strength function: 1 SV () =- Im V ( x) A( x, x ',)V (i)


(

eff

1 ( x,) =- Im

)

free p-h propogator

effective operator
eff

V

eff

( x,) =V (x) + F A(x, x ',)V


( x ',)


p-h interaction

(ii)

transition density:
2

( x,) is defined by SV () = (V (x) ( x,) ) ;
(iii) DSD-reaction amplitude:
M c () :
2

(

cont

(x)V

eff

( x,)

bound

( x)

)

set of the reaction-channel quantum numbers

M c () = SV () - the unitary condition;
c
5


(iv)

energy-averaged quantities with taking the spreading effect into account:

S () = S ( + iI / 2) ,

(x,) = (x, + iI / 2) ,

M c () = M c ( + iI / 2) .

(v)

effective accounting for contribution of isovector momentum-dependent forces by scaling transformation:
% S ( ) = 1 S 1+kL 1+kL

transformation changes EWSR, but doesn't change NEWSR (see below) _________________ Within the approach all observables are calculated with the use of the properly modified CRPA eqs.

6


2. Methods (continuation) Probing operators and sum rules
L =1
(in the abcence of m.-d. forces)

V1(i)( x) = rY1

(i)

;



(i )

=

{

(+)

,

( 3)

,

(-)

}

:
.

V 3 =0 T

2 (3 ( EWSR1 ) = S13) ()d = 3 h A . 8 m

Overtone (isovector partner of the ISGDR):
(3 V1,o)v ( x) = r(r 2 - )Y1 (3 EWSR1,o)v (3)

;
4

( V1,(3) ( x)13) ( x,m ) = 0 . ov

(

)

1 h2 = A 11 r 8 m

{

- 10 r

2

+ 3

2

}

T = ±1 3
( ( NEWSR1 = S1 -) ()d - S1 +) ()d = r 4n(-) (r )dr ( ( ( EWSR1 = S1 -) ()d + S1 +) ()d = EWSR13) + r 4n(-) (r)U C (r)dr

L = 2,

T = 0 3
(3)

(3 V2 ) ( x) = r 2Y2

,

2 (3 EWSR2 ) = 5 h r 2 . 4 m
7


Isospin splitting of the IVGDR(3) in not too-heavy nuclei
T> = T + 1
(3 " IVGDR> ) =

1 ( 2T +2

-)

( IVGDR1

+)

",

(3 ( S> ) () = 4 S1 +) ( - C ) ; 2T + 2

Pauli blocking

Coulomb displacement energy

(3 ( (3 EWSR> ) = S>3) ()d y> EWSR1 )

T< = T

(

y

> <<

1)

(3 ( (3 ( EWSR< ) = (1- y> ) EWSR13) S< ) () ; (1- y> ) S13) ()

Isovector momentum-dependent forces lead to:
(3 ( (3 EWSRL ) EWSRL3) = (1+ kL ) EWSRL ) ;

scaling transformation

NEWSR is independent of the forces. ________________

Below the properly modified quantities are only considered.

8


Cross sections of simplest photonuclear reactions (i)
V
( E1)

E1-photoabsorption 2 =- 1V1(3) ; B =16 3 e 3 hc 2
( E1)
> ()(1- y> ) ; a =

< a = BS

a ()
(ii)

B S (+) ( - ) C N -Z +2 1

exp a

I , k1 are adjusted.

DSD (n)- and (n)-reactions via the IVGDR< (bound by the detailed balance principle)

< d µ (,) 1 < = µ ()(1+ a2 ()P2 (cos ) ) ; 4 d


µ () = B M
c < ( E1) c( µ )

M

( E1) c( µ )

,M

( E1) c '( µ )



()

2

(1- y> )

(iii) SD (p)-reaction via IVGDR> (specific double GR)

µ () = B M
c

>

( E1) c(µ )

() ; M

2

( E1) c( µ )

()

V

(+)eff

( - C ) 1 , vtr = v IAS N -Z +2 N -Z +2
symmetry potential
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(iv)

Asymmetry (relative 90°) of the (n)- and (n)reaction differential cross sections in the vicinity of the IVGQR
(3)

V
V

( E1)
( E 2)

M

( x) =1- r 2Y2 M 2 =

( E1) () c (3)

(DSD) ;
( E 2) c

() (SD)

d µ (,) d

L , L '=1, 2; N = 0- 4



LL AN ' ()PN (cos )


[ d µ-] µEx d E (,1) = ; [+ ] x d µ µEx d

M

( E1) c( µ )

(),M
( E1)

( E 2) c '(µ )

()


terms with N =1,3 are due to interference of M

,M

( E 2)

1 = 55o, P2 ( 1 ) = P2 ( -1 ) ; 0

d

µ

[m ]

= d µ (1) md µ ( - 1)

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3. Results ·

( 48Ca, 90Zr, (Fig. 1)

140

Ce,

208

Pb )

E1-photoabsorption

a ()

In the following no new parameters. · Gross properties of the IVGDR multiplet
(3)
(3)
( m)

(i) IVGDR
(ii) IVGDR (iii) IVGDR

(3) : 1 (r , m )

(Fig. 2) (Figs. 3,4)

2(

208

(3) (3) Pb): S1,ov () , 1,ov (r , m )

( 90Zr): S1( m) ()
( m) m

(Fig. 5)
( m) m,exp



(Table 1)

(iv) IVGDR

(3) >
> m



> ,< a

() ( 90Zr, Fig. 6);
(3)
208

(Table 1) (Table 2)
(3) 2

Isolated T> 1--resonances (iv) IVGQR (

Pb): S(3) () ; 2

( r , m )

(Figs. 7,8)
(3)

·

DSD photoneutron reactions in the vicinity of the IVGDR
208

Pb(nµ)-reaction cross sections (calculated) (Fig. 9)
d µ ( n ,=90°) d
11

(n µ ),

(Figs. 10,11)


·

DSD(via IVGDR
90

(3) <

) + SD(via IVGDR

(3) >

) (p0)-reaction

Zr(p0)

(Fig. 12)
208

·

Asymmetry of the IVGQR
x

Pb(n)-reaction and

208

Pb(n 0 )-

reaction differential cross sections in the vicinity of the
(3)

E (,55°)
nat

E x < 2 MeV (Fig. 13a) E x < 4 MeV (Fig. 13b)

target

Pb
n (,55°)
0

(Fig. 14)

12


4. Summary We realized the main aim of the presented work: semimicroscopic description of (i) the DSD phootneutron reactions, accompanied by excitation of the IVGDR< ; (ii) the direct proton decay of the IVGDR> components; (iii) the asymmetry (relative 90°) of the of the (n)and (n)-reaction differential cross sections in the vicinity of the IVGQR . Abilities of the approach in description od the main properties of the IVGDR multiplet (including the IVGDR2) and the IVGQR have been also checked.
(3)

13


Table 1. Calculated and experimental energies (in MeV) of the IVGDR ( ± ) , IVGDR (3) . Total neutron branching > ratios for the IVGDR

48

(3)

.

(+) m

(-) m,<



(3) m,>

btot ,% n
calc. 21.4 4.1 9.9 8.4

Ca

calc. 21.3

exp. -

calc. 18.5

exp. -

calc. exp. 26.3 25.8

90

Zr 25.15 25.4(0.5) 7.55 10.4(1.8) 20.1 21.2 Ce 24.4 (25.3) no prominent giant resonance

140

208

Pb 26.1 26.6(0.5)

Table 2. Parameters of the T> 1--resonance, studied via the (e,e'p)- reaction (Richter et al., 1997)
r , MeV
, eV
0



p

, keV
0



p

, keV
0

calc. 16.0 16.5 17.0

exp. calc. calc. calc. exp. exp. exp. 16.28 170 108(35) 55 54(18) 25 20(5) 160 318 7 14 150 70 -

14


a(), m b
48
100

Ca

400 300 200 100

140

Ce

50

0 5 250 200 150 10 15 20 25 30 35

0 5 800 10 15 20 25 30

90

Zr

20 8
600

Pb

400 100 50 0 5 10 15 20 25 30 35 200

0 5 10 15 20 25 30

, M e V



arb. u.

1,ov

( r , m )

208

Pb

0

2

4

6

8

10

12

r, fm

14

1 (r, m )
arb. u.

48 90 14 20

Ca Zr 0 Ce 8 Pb

0

2

4

6

8

10

12

14

r, fm


5

S

1,ov

()/EWSR, % MeV

-1

208

Pb

4

3

2

1

0

10

20

30

40

50

60

70

, M e V


5

_ _ (-) ~ (-) -1 S (), S (), M e V fm

2

90

Zr

4

3

2

1

0

10

20

30

40

50

, M e V

2.0

_ _(+) -1 ~ (+) S (), S (), M e V fm

2

90
1.5

Zr

1.0

0.5

0.0

0

5

10

15

, M e V

20


250

a(), m b

90

Zr

200

150

100



<

50


10 15 20 25

0

>
30

, M e V


S ( ), M eV fm
600 500 400 300 200 100 0

(3)

-1

4

208

Pb

m =21.5 M e V

12

14

16

18

20

22

24

26

28

30

, M eV

(r,m)
arb. u.

(3)

208

Pb
(3 )

IV G Q R

0

2

4

6

8

10

12

14

r, fm


25

4 d µ /d , m b /s r ( =90 )

o

208

Pb

µ
3 3 2 1 2

-1

20

15

p 1/2 p 3/2 f5/2 i13/2 f7/2

10

n= +

µ

5

0 10 15 20 25

, M e V

30


900

4 d /d , µb/sr (=90 o)
89

90 0
14 0 5/2

Y 2d

Ce 2 f

7/2

600

60 0

300

30 0

0

6

8

10

12

14
89

16

18

0
2500

6

8

10

12

14

16
14 0

18

20

3000 2500 2000 1500 1000 500 0 6 8 10 12 14

Y all

2000 1500 1000 500 0

Ce all

16

18

6

8

10

12

14

16

18

20

n, M e V


4 d /d , µb/s r (=9 0 o)
80 0

20 8

Pb
40 0

60 0

2g

9/2

1i
20 0

11 /2

40 0

20 0

0 80 0

6

9

12

15

18

0 80 0

6

9

12

15

18

60 0

1j

15 /2

+ 3d

5/2

60 0

2g 7/2+ 3d

3/2

40 0

40 0

20 0

20 0

0

6

9

12

15

18

0

6

9

12

15

18

n, M e V


12

p (), m b
0

10

8

6

4



2

<



>
25 30

0 15 20

, M e V


( ,5 5 )
208

o

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 20

Pb (,n ) E x<2 M e V

a)

b)

208

Pb (,n ) E x<4 M e V

22

24

26

28

30

, M eV


1.0

( , 5 5 )

o

208

Pb (n ,0)

0.8

0.6

0.4

0.2

0.0

-0 .2

6

8

10

12

14

16

18

20

22

24

, M eV