~:~ NUCLEAR PHYSICS A

ELSEVIER Nuclear Physics A 628 (1998) 597-606

Disintegration of the deuteron by linearly polarized photons at low energies

V.P. Likhachev 1, M.N. Martins 2, Yu.A. Kasatkin 3, M.T.F. da Cruz, J.D.T. Arruda-Neto, V.B. Shostak 4, V.V. Denyak 3, I.G. Evseev 3,

S.A. Paschuk5 V.M. K h v a s t u n o v 3 Laboratdrio do Acelerador Linear, lnstituto de F{sica da Universidade de Sdo Paulo, Caixa Postal 66318,

05315-970 Sdo Paulo, SP, Brazil

Received 4 July 1997; revised 20 October 1997; accepted 30 October 1997

Abs t rac t

The cross section and the ~V-asymmetry of the reaction d ( ~ , p ) n were measured in the energy interval Ey = 5-10 MeV. Cross sections dO-ll and do-± were derived from the measured quantities dtr0 and 2'-asymmetry. The results are compared with theoretical calculations available for this energy region. (~) 1998 Elsevier Science B.V.

PACS: 25.20.-x; 25.10.+s Keywords: Photodisintegration: Deuteron; Polarized photons; Angular distribution; Cross section

1. Introduct ion

The p h o t o d i s i n t e g r a t i o n o f the deu te ron is a power fu l tool to s tudy the n u c l e o n -

nuc l eon in te rac t ion , he l p i ng to p robe the var ious NN-po ten t i a l s . The a d v a n t a g e of this

k ind o f e x p e r i m e n t is tha t it c o m b i n e s the w e l l - k n o w n e l ec t romagne t i c in te rac t ion and

the s imp les t nuc lca r aggrega te . T he m e a s u r e m e n t of the deu t e ron d i s in tegra t ion is usual ly

I On leave from Kharkov Instilute of Physics and Technology, Ukraine. 2 E-mail: martins@if.usp,br 3 Kharkov Institute of Physics and Technology, Ukraine. 4 Kiev Institute of Nuclear Physics, Ukraine. 5 On leave from Kharkov Institute of Physics and Technology, Ukraine. Present address: Centro Federal de

Educa~fio Tecnoldgica do Paranfi, Curitiba, PR, Brazil.

0375-9474/98/$19.00 @ 1998 Elsevier Science B.V. All rights reserved. PII S0375-9474 (97 ) 00620-9

598 VP Likhachev et aL /Nuclear Physics A 628 (1998) 597-606

a test case for new experimental techniques, assessing new methods while: helping to increase knowledge about the strong interaction.

The interpretation of the low-energy breakup data presents problems common to higher energies, like (a) the choice of observables sensitive to the NN-force properties and their description, and (b) the introduction of non-nucleonic degrees of freedom, like meson- exchange currents (MEC) and relativistic corrections to the one-body current [1]. Effects like final-state interaction (FSI) must also be taken into account.

The near-threshold region is particularly remarkable, due to simplifications on both theoretical and experimental aspects, as (a) the presence of a single dominant multipole (usually E1 or Ml) with negligible contributions from other multipoles in the entrance channel; (b) each multipole taking few partial waves in the exit channel, and (c) the absence of background from competitive channels or reactions. Those aspects help to simplify the analysis of experimental results in this energy region.

The use of polarized photons is particularly interesting because polarization observ- ables contain interference terms between reaction amplitudes and are sensitive to small amplitudes belonging to contributions of non-nucleonic degrees of freedom. Although at low energies those amplitudes present a small relative contribution, this is compensated by the excellent accuracy achieved by the experimental data obtained in this energy re- gion. FSI effects, on the other hand, are strong close to the threshold and thus convenient to be studied.

This work presents results of the deuteron photodisintegration cross section and the X-asymmetry, measured with linearly polarized photons on the near-threshold energy region. The data are compared with calculations performed in the framework of the Lorentz- and gauge-invariant [2-5] and diagrammatic [6] approaches, and the Par- tovi [7] and Laget [8] models.

2. General definitions

The differential cross section for the reaction d(y, p )n (see Fig. 1 ) can be written in the center of mass system (CM), and in the case of partial polarization, as [7]

do- dcr° "0 P doq d--~(Op, ,15, E~) = - ~ { p, E~) + ~ d12 (Op, E~) co s2 5 , (1)

z K(Ko,~) ~ " plE,P') e~. d{Do ~') n (E,-P*) x ~-

(e) (b)

Fig. 1. General notation.

gP Likhachev et al./Nuclear Physics A 628 (1998) 597-606 599

where Pr is the degree of linear polarization of the photon, Op is the angle between the momentum of the photon and that of the outgoing proton, and ~b is the angle between the polarization vector of the photon ( 3 and the x-axis (see Fig. lb) ;

do'o 1 (do-II(Op,E ~) do-±(Op,E~) ) d ~ (Op'Er) = 2 \ d ~ + dr2 ' (2)

and (do`l/ds2) is the part of the differential cross section which characterizes the azimuthal asymmetry. Here we have used the following notation for the differential cross sections:

d~rll do- do-± _ d o dJ? - d ~ (& = 0° ) ' d/2 d1"2 (~b = 90°) " (3)

In terms of the azimuthal cross section asymmetry (X-asymmetry) the differential cross section becomes

do" do-0.0 -~(Op,d?,Er) = ~-~( p,Er) [1 + PrX(Ot,,Er) cosZ~b] (4)

where

( do`l /d~) ~Y ( Op, Ez, ) - ( do`o/d~)

I (do`ll/df2) - (do-±/dl2) I

P~ ( do`ll/df2) + ( do` ±/dJ2) " (5)

For complete linear polarization, Pr = l, and with a convenient choice of directions, the differential cross sections can be written as

do" H do`0. O~ dg2 (O,,Ew) --- j-~( ,,E~,) [1 + X(Ov, E:) ]

do'± do'o . dr2 (Op, E~) = ~--~(Op, E~) [1 - X(Op, E~)] . (6)

The differential cross section for non-polarized photons can be expressed in terms of the parameters measured in the experiment as

dgo AN

d~(2 = N,, (dNy/dEr) AErAg2 ' (7 )

where AN is the number of protons produced by photons in the energy bin AE~, N~ is the number of nuclei per cm 2 of the target, (dN~/dEr)AE~ is the number of photons in the energy bin AEr, and As2 is the detector solid angle.

The experimental uncertainties of the cross sections can be calculated in the following way:

2 }j2 _4\ d D ) A (l_q:X) t + (zlX) 2 \ a n / ] \ ds~ , (8)

where A(do`o/d~2) and AX are the experimental uncertainties of the non-polarized cross section and X-asymmetry, respectively (which must have been obtained in statistically

600 v.P Likhachev et al./Nuclear Physics A 628 (1998) 597-606

independent measurements, to avoid correlations). The uncertainty in 2?-asymmetry can

be written as

1 [ (Ntl - N ± ) 2 A ~ - 2 P y N o L ( A N I { ) 2 + ( A N ± ) 2 + p2 (AP~')2+(Nll -N±)2 (ANO)2] ' / 2

No J ' (9)

where AP~,/P r is the relative uncertainty of the degree of linear polarization; Nil4_.0 and ANII,±.o are the experimental yields and corresponding uncertainties for the parallel,

perpendicular and non-polarized cases, respectively. The uncertainties in the yields are

given by

= ~/(RI[,±.o + 1)Nil.±,0, (10) ANH,±.o

where Rli,±,o is the random-to-true coincidence ratio for each polarization situation.

3. Exper imenta l p r o c e d u r e

The experiment was carried out in the direct beam of the Kharkov 2 GeV linac

(Fig. 2). The experimental facility and the main characteristics of the beam were

described in Refs. [9,10]. Some preliminary results (with about 1/3 of the statistics now presented) were described in Ref. [ 1 1 ]. In this work only those aspects relevant

to this particular deuteron experiment will be presented.

The linearly polarized photons were produced by channeling an E0 = 1 GeV electron

beam, with 10 -4 tad divergence, through the (110) plane of a 500 /xm thick silicon

crystal. The crystal was oriented with respect to the electron beam direction by a goniometer with accuracy better than 5 × 10 .5 tad. The orientation was controlled bv

a thin ionization chamber, tuned to be sensitive to the low energy part of the photon spectrum. The photon beam was collimated to a diameter of 5 mm at the target position

and the photon flux was measured after the target by a quantameter.

The target consisted of a chamber filled with gaseous deuterium at pressures of

0.5× 105 and 4× 105 Pa, with thin aluminium toil windows for the incoming and outgoing

beams. The gas pressure and temperature were controlled during data acquisition.

Fig. 2. Experimental layout. 1: goniometer with monocrystal target; 2: bending magnet; 3: shielding walls; 4: photon collimator; 5: cleaning magnet; 6: deuterium chamber with detector, collimator and cobalt-samarium magnet; 7: ionization chamber; 8: quantameter.

~t~ Likhachev et al./Nuclear Physics A 628 (1998) 597-606 601

The emitted protons were detected by a silicon surface barrier detector 100/tin thick

and with 20 mm in diameter. The detector was shielded with lead, having a defining

collimator in the front, and a cobalt-samarium permanent magnet acting as a filter fi)r

low energy electrons. The whole system was placed inside the deuterium chamber in

order to keep the detection threshold for protons as low as possible. The interaction volume seen by the detector was restricted by an additional collimator, in order to limit

proton emission angles to the interval 85 ° < Op < 95 ° in CM. Proton energy spectra were measured in three different crystal/beam configurations:

two with the (110) plane of the crystal oriented to produce photons polarized either

parallel (N N ) or perpendicular (N±) to the reaction plane, and the third with the crystal non-oriented (No). The energy spectra were corrected for proton energy losses along

the path from the point of interaction to the detector.

In order to achieve similar statistical accuracy along the energy spectrum, in spite

of the decreasing character of both the breakup cross section and the photon spectrum,

lower energies were measured at deuterium gas pressure of 5 x 104 Pa, while for higher energies the gas pressure was raised to 4 x 105 Pa. The energy binning intervals, where

data were averaged, were also increased with increasing photon energy. The incident photon energy was kinematically reconstructed from the measured energy

of the proton, assuming two-particle deuteron breakup [ 12].

The contribution from reactions including mesons in the final state is small due to

both the abrupt decrease of the photon spectral intensity with increasing Er (~ I/Er), and the smaller cross section of this reaction. Protons from those reactions are extracted

from the spectrum at a latter stage of the data reduction. Fig. 3 shows the shape of the photon spectrum, in terms of what is called magnitude of

the coherent effect [13], defined as the ratio of the photon spectral intensities obtained

for oriented (plane [ 110] ) and non-oriented crystal configurations:

NII(E~, ) q- N±(Ez, ) /~(E~) =

2N0(E~)

The non-oriented configuration means that the goniometer is rotated just enough to eliminate the coherent peak. The lilting is such that the bremsstrahlung background

can be considered unaltered, since the crystal thickness, as seen by the electron beam,

remains essentially the same. The spectral intensity for the oriented crystal configuration

presents the coherent peak around 6 MeV and goes down to the amorphous level around 20 MeV. The coherent peak is about 6 times higher than the amorphous level and presents a maximum intensity of about 4 x 10 l° MeVls- lcm -2. Since the coherent

intensity converges to the amorphous level much below the meson threshold, the yield

from reactions with mesons in the final state, due to the coherent part of the spectrum N~.± (E~,) = NL±(E~) - No(E~), is negligible.

The magnitude of the coherent effect,/3, allows the evaluation of the degree of linear polarization of the beam [ 13 ]

602 V.P. Likhachev et al./Nuclear Phyxics A 628 (1998) 597-606

I I I I ~ - -

5 ÷

t,

1 i ,9 i ll2 I I 0 2 4 6 10 14 16 18 20

E,y( UeV ) Fig. 3. Spectrum of photons produced by 1 GeV electrons passing through the expressed in units of the intensity of the corresponding amorphous spectrum.

110) plane or a Si cryslal,

where pC" is close to unity and represents the degree of polarization of the coherent part of the spectrum. The degree of linear polarization of the beam (coherent plu,; amorphous spectra, see Eq. ( 11 )) changes significantly with photon energy, from ~83% at E:~ = 5 MeV to ,-o66% at 10 MeV. In the energy range cow,'red by our experiment, the degree of polarization of the coherent part of the spectrum,/~' , presents a negligible dependence on the photon energy [13],

x 2 P ~ : ~ - ' I - y + . . . .

where x = ET/Eo (in our conditions 0.005 < x < 0.01 ). The X-asymmetry can be obtained from the coherent part of the photon spectra by

XCl' ( E~ ) - UC ( ET )

L - - J

where pC ~ I is the degree of linear polarization of the coherent part of the photon spectra (see Eq. ( 11 ) ).

To check for a possible contribution to the X-asymmetry from the amorphous part

of the spectrum, this quantity was also measured with the crystal in the non-oriented configuration. The results (0.003 ± 0.003) show an asymmetry compatible with zero. We then evaluate the systematic uncertainty of X-asymmetry as being less than 0.006, within a confidence level of 80%.

Since the experiment measures only the product P y C ( E T ) ~ ( E T ) , t h e following pro- cedure was used for the extraction of V(Ey). We used the data of Ref. [14] on 2-asymmetry at E~, = !;}.9 MeV to determine pC at this energy. The absolute data of Ref. [ 14] were obtained using a practically 100% linearly polarized (P:, = 0.999) and

V.R Likhachev et al./Nuclear Physics A 628 (1998) 597-606 603

monochromatic photon beam from Compton backscattering of laser light on high en-

ergy electrons. We actually use our reaction at this energy as a polarimeter in order to

determine the degree of polarization of the coherent part of the beam. This parameter,

according to channeling radiation theory [15], presents a negligible dependence on the

photon energy, in the range of interest of this experiment. We then assumed that pC

is constant in the range 4 -10 MeV, and used the value obtained at E~, = 9.9 MeV to

determine 2;-asymmetry over this energy range.

The cross sections (da%l/dS2)(E~) and (do-±/ds?)(E~) can not be accurately mea-

sured in our experiment since we do not measure directly the photon spectrum of

channeling radiation (only its integral) . We have used Eq. (6) and the measured values

of (dcro/df2) (E7) and ,.V(E~,) to obtain (d~rjl,±/df2) (ET). (do'o/dO) (Er) was calculated from Eq. (7) , using the Schiff expression for the shape

of the bremsstrahlung spectrum [ 16] (the intensity was determined experimentally with

the quantameter, with accuracy better than I%) and zls2 = 3 .22(4)10 -2 st, obtained

by Monte Carlo simulation of the reaction events in the target volume [ 17]. The total

absolute uncertainty to (do'o/dO) is ~3%. The main contributions come from the

uncertainty in the determination of the effective solid angle (which includes the target

thickness [17] ) and the bremsstrahlung spectrum shape. (dcro/df2) was normalized to

the world data of Ref. [ 18] at E,, = I0 MeV, the normalization factor being 1.037.

4. Results and discussion

The values of .~'-asymmetry for Op = 90 ° obtained in the present work are shown in

Fig. 4 as circles. Results of calculations available in this energy region are also shown.

Curves 1 and 2 represent calculations carried out in the Lorentz- and gauge-invariant

(LGI ) approach [ 2 - 5 ] , using deuteron wave functions ( D W F ) corresponding to Paris

potential [ 19] and relativistic Gross ' wave function 120] (undisl inguished) with and

1.00 ~ r

1

0.96

r,q

0 9 4

O Q2

0.9( ' I ' I 2 3 4 5 6 7 8 9 10

ET( M e V )

Fig. 4. ~'-asymmetry for 0 v = 90 ° versus photon energy. Curves 1 and 2 represent calculations in the LGI approach for Paris and Gross DWF (results undistinguished) with and without FSI, respectively. Curves 3.4 and 5 represent calculations in the diagrammatic approach for one-body approximation and with successive addition of meson exchange current with plane wave a p state (MECPW), and MEC with final state n-p interaction (MECFSI), respectively.

604 ~P. Likhachev et al./Nuclear Physics A 628 (1998) 597-606

650

6OO

-~ 550

500 o O~

H 450

b ~ 400

35o

300 3

I I I

1

x

_ _ L ~ I _ _ ~ - I I I

4 5 6 7 8 9 1

Ey( MeV

Fig. 5. Differential cross section (d~rll/dII)(Ee) for 0p = 90 °. Curves 1 and 2 represent calculations in the LG1 approach for Paris and Gross DWF, respectively, with and without FSI (undistinguished).

without FSI, respectively. The pn-rescattering amplitudes (FSI) include the contribution of the 1 So resonance, with Breit-Wigner parameters GR = 300 keV, MR = m l, + m, + IR and IR = 0.067 MeV, plus background calculated according to the approach of Ref. [21 ]. Curves 3, 4 and 5 represent calculations in the diagrammatic approach [6], for one- body approximation and one-body approximation with the addition of meson exchange currents (MEC) with plane-wave n-p state (MECPW), and MEC with final state n- p interaction (MECFSI), respectively. The DWF and N-N scattered amplhudes were calculated in this work for the Bonn OBEPR model of the N-N interaction [:22]. In the energy range 5-10 MeV the S-asymmetry presents small sensitiveness to the different theoretical predictions. All curves lie inside a ±2% band, but the accuracy reached by

the experiment allows some analysis. The calculation in the diagrammatic approach [6] with MECFSI (curve 5 of Fig. 4), is in better agreement with the data than the analogous calculation in the LGI approach (curve 1) which slightly overestimates the values of 2--asymmetry. On the other hand, the LGI without FSI (curve 2) agrees well with the experiment.

Figs. 5 and 6 present the cross sections (dCrll/dt2)(Ee) and ( d ~ r z / d s 2 ) ( E r ) , re- spectively, as open circles. As stated before, these were obtained (see Eq. (6)) from the experimental data on ( d o ' o / d O ) ( E r ) and ~V(Ez, ). Fig. 5 also shows results of cal- culations in the LGI approach [2-5] . Curves 1 and 2 correspond to Gross and Paris DWE respectively. The calculations are not sensitive to the inclusion of FSI. The data agree better with the calculation using Paris DWE

In Fig. 6 we show data for (dO'_L/d,(2)(E~,O p = 90 °) together with experimental data (Refs. [ 23-26], triangles) and calculations for (d~ro/d$2) (E~,, 8p = 0 °). These quantities are amenable to comparison due to the fact that ( d o o / d I 2 ) ( E r , 6P I, = 0 °) = (do -±/ds2 ) (Er , 0p = 0 °) and that (do-j_/ds'2)(Er, ~p) has a very mild 0p dependence, about 0.5% between 0 ° and 90 °, according to LGI calculations. The forward direction equality is a consequence of the singlevaluedness of the differential cross section. The agreement between the two sets of experimental data, obtained in two dilferent and

EP Likhachev et al,/Nuclear Physics A 628 (1998) 597-606 6(15

12 i I I - -

10

O 8 2 4

)

12

Ey( M e V )

Fig. 6. Differentia] cross sections (dc r j _ /d f l ) ( Ey ) for 0p = 90 ° (present work, circles) and (do o/d[,2 ) ( £,y ) for 0j, = 0 ° (Refs. 123-261, triangles). Curves 1-5 are the same as in Fig. 4; curve 6 is from Ref. 171; and curve 7 from Ref. 181.

independent experiments, is remarkable. The data lie between curves 1 and 2 (LGI with and without FSI) but show good agreement with curves 4 ,and 5 (diagrammatic

approach with MECPW and MECFSI, respectively) and curve 6 [7]. The error bars in Figs. 4-6 represent only statistical uncertainlies. Possible system-

atic errors, connected with the absolute value of (i) the cross ,;ections and (ii) the

polarization degree, are not presented.

5. Conclusions

Low energy photon beams with high intensity and high degree of linear polarization

can be obtained as a result of plane channeling of ultrarelativistic electrons in a Si crystal. The intensities achieved (~4 x 10 I° MeV -j s - l cm-2) allowed the measurement

of the .S-asymmetry and the differential cross section of the reaction d(~,p)n, using a

low-pressure gaseous deuterium target, with approximately 1% statistical accuracy. The X-asymmetry data are well described in the framework of the diagrammatic

approach for MECFSI. An analogous calculation in the LGI approach slightly overesti-

mates the data.

The data for (do-ii/df2)(E~,) are in good agreement with the calculation in the LGI

approach using Paris DWE The calculated (dCrll/dS'2) (E~,) is not sensitive to FSI effects. The data of (dcr±/dS2)(ET) for 0p = 90 ° are consistent with the data obtained with

nonpolarized photons (do'o/dO)(E:,), for Op = 0 °. Both sets of data agree well with calculations in the diagrammatic approach using the Bonn model and MEC with and

without FSI. These two calculations are indistinguishable in the energy region of the measurements.

Acknowledgements

This work was supported in part by FAPESP, CNPq and FINEP.

606 VP. Likhachev er al./Nuclear Physic* A 628 (1998) 597-606

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