Critical review of the present experimental status of neutron-proton scattering up to 1 GeV

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Critical review of the present experimental status of neutron-proton scattering up to 1 GeV

C. Lechanoine-Leluc, F. Lehar, P. Winternitz, J. Bystricky

To cite this version:

C. Lechanoine-Leluc, F. Lehar, P. Winternitz, J. Bystricky. Critical review of the present experimental status of neutron-proton scattering up to 1 GeV. Journal de Physique, 1987, 48 (6), pp.985-1008.

�10.1051/jphys:01987004806098500�. �jpa-00210528�

Critical review of the present experimental ^{status of} neutron-proton scattering up ^to 1 GeV

C. Lechanoine-Leluc, ^{F. Lehar}

(+),

^P. Winternitz

(*)

^{and J.}

Bystricky (a), (++)

DPNC, l’Université de Genève, Geneva, Switzerland

(+) ^DPhPE, CEN-Saclay, ⁹¹¹⁹¹ Gif-sur-Yvette, Cedex, ^France

(*) Centre de Recherches Mathématiques, Université de Montréal, ^C.P. 6128, Montréal, Québec, ^Canada

H3C 3J7

(++) ^{UCLA, Los} Angeles, California 90024, ^USA

(Reçu ^{le 9} septembre 1986, accept,6 ^sous forme definitive ^{le 4} fevrier 1987)

Résumé. ²⁰¹⁴ La situation expérimentale de la diffusion élastique n-p ^aux énergies jusqu’à ^{1 GeV est} passée

attentivement en revue, ^en insistant tout particulièrement ^{sur les} questions auxquelles ^devront répondre ^de

futures expériences. ^La question des tests à faire pour vérifier les symétries fondamentales est traitée

(invariance ^sous renversement du temps ^et conservation du nombre isotopique). ^{Une revue très} complète ^des

résultats est faite. On voit que ^ces résultats sont trop peu nombreux ^{sur toute} la gamme d’énergies considérées et même parfois contradictoires. Les valeurs des déphasages ^{obtenus à} partir ^{de cette base} incomplète changeront ^{d’une manière} appréciable quand ^{de nouveaux résultats seront} inclus. Bien entendu aucune

reconstruction directe des amplitudes de diffusion np n’est possible actuellement.

Abstract. ²⁰¹⁴ The present experimental ^status of elastic neutron-proton scattering ^at energies up ^to 1 GeV is reviewed. Open questions that should be answered by ^{a new} generation ^of experiments ^are emphasized. ^These

include detailed tests of fundamental symmetries, ^{such as} time reversal invariance and isotopic spin

conservation. Experimental ^{data are} reviewed and shown to be insufficient over the whole energy range and sometimes inconsistent. Therefore phase shifts solutions will probably change significantly ^{once new data are}

included. Of _course, no direct amplitude reconstruction of np scattering ^is possible yet.

Classification

Physics ^Abstracts

13.75

1. Introduction.

The purpose of this article is to

provide

^{a critical}

analysis

^{of the} present ^{status of} neutron-proton

scattering

ⁱⁿ the energy

region

^{from zero to about}

1 GeV. It is an

appropriate

^{moment for such a}

review since a new

generation

of np elastic and inelastic

scattering experiments

^is

presently

^{in pro-}

gress ^{or in}

preparation

in various laboratories. We shall summarize what is

already

^{known about the} np system ^{and what we can}

hope

^{to learn in the near}

future.

The type ^of

question

^{that new}

(and old) experi-

ments on np

scattering

^{should answer are :}

i)

^{What are the}

symmetries

of np

scattering ;

ⁱⁿ

particular

^{how well are}

parity

conservation, ^time reversal invariance and

isospin

conservation ob- served.

(a ) Permanent ^{address :} DPhPE, CEN-Saclay, ^France.

ii)

^The existence and character of non-strange

dibaryons,

ⁱⁿ

particular

dinucleons with .

isospin

1= 0. In the same context, ^a check of the accuracy and

reliability

of various

three-body

^{and other}

model calculations

explaining

^the occurrence of

dibaryon-like phenomena

^without

introducing

6

quark

^states

(with

colour distributed over six rather than three

quarks).

The best answer to the above

questions (and

^any

other

questions concerning

^the nucleon-nucleon sys-

tem)

^{would be}

provided by

^a

complete

reconstruc- tion of the _pp and _np

scattering amplitudes

^{over a}

large

energy

region.

While the situation in this

respect ^is

already satisfactory

^for pp

scattering (at

least between 400-800

MeV)

^{the same cannot be said}

for np

scattering.

For elastic np

scattering

^{the overall}

aim should be to perform

sufficiently

many

experi-

ments to be able to reconstruct the np

scattering amplitudes directly

^{at least at several}

energies

^and

angles

^{and to be able to}

perform

^a reconstruction via

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01987004806098500

energy-dependent phase

^shift

analysis

^{or some other} formalism, ^{for all}

angles

^{and all} energies ^{in the}

considered

region.

The reason why ^{it is}

possible

^to

speak

^{of a « new}

generation

^{» of} np

experiments

^{is the}

availability

^of

new sources of

polarized

^{neutron beams at}

laboratories that are also

making

^{use of}

polarized

proton targets

(e.g.

^Satume II, SIN, LAMPF,

TRIUMF).

Current information on np ==> np

scattering

^was

mainly

obtained either

by scattering

^free

(polarized

or

unpolarized)

^{neutrons on a}

(polarized

^{or un-}

polarized) hydrogen

target, ^or

by quasifree scattering

of protons ^{or neutrons bound in} deuterons. A new

feature is the use of a

polarized

deuteron beam considered to be a simultaneous beam of

polarized

protons ^and neutrons, ^{scattered on a} proton target

[1].

^{We remark that neutron beams are}

usually

not monochromatic. The

interpretation

^of

quasielas-

tic

scattering

^{tends to involve}

systematic

^uncer- tainties, ^{due to}

(possibly large)

^Glauber type ^correc- tions. These are

particularly important

^{for cross}

section measurements. A

comparison

of free and

quasifree

pn

polarization

data indicates that these corrections tend to cancel out in

polarization

^ex-

periments.

^{An extension of} Glauber corrections to the case of

polarized particles

would, ^{on the other} hand, ^be very

important.

All three above types of np ==> np

experiments

provide valuable contributions to the data basis.

Existing analyses

^{of np data treat} np and pn ^scatter-

ing

in similar _ways. The data

points

^consist

mainly

^of

total and differential cross section

(82

^{% of all}

data).

The data basis is too sparse ^to allow a direct reconstruction of the _np

scattering amplitudes (at

any energy and

angle).

Phase shift

analysis

of np data has

only

^been

possible

^{under the}

assumption

that the

isospin

^{I =1}

phase

^{shifts are well deter-}

mined from the pp data. The np data ^are then used to determine the I ⁼ 0

scattering amplitudes only.

The

phase

^{shifts are} obtained from insufficient data and will

probably change significantly

^{once new data}

appear and ^are included in the

analysis.

When

discussing experimental

data in this paper

we will make use of two different sets of

phase

shifts : the

Saclay-Geneva analysis ([2],

and that of

Arndt [3]).

The first is used

systematically,

^the

second

mainly

^to indicate differences in

predictions, showing

that the np system ^{has not} been measured

sufficiently. Throughout

^{the article we use a four}

index notation and a formalism

presented

ⁱⁿ

previous publications [4-6].

^{For data}

published

^before

April

1981 we refer to the

compilation [7] (reference

^to

data

already

^{included in Ref.}

[7]

^are

given

^{in the}

same manner as in Ref.

[7],

e.g.

78/B-200/).

Throughout

^{the text T} denotes the kinetic energy of the incident

particle

^{in the}

laboratory

system. ^The

same

quantity

^{is denoted}

Tkin

^{in the}

figures.

In section 2 we discuss the status of discrete

symmetries ⁱⁿ np

scattering

^{and the}

possibility

^of

further

experimental

^tests. In section 3 we

specify

the

simplifications

^{that occur in}

particular

^kinemati-

cal situations, ^{such as} forward and backward scatter-

ing,

^for 8CM ⁼

1T/2

^and

scattering

^{at the elastic}

threshold. The main features of

existing

np ^{data are}

analysed

ⁱⁿ section 4 where we discuss the data in

conjunction

^with

phase

^shift

analysis interpretations.

Possible

dibaryonic

resonances are not discussed in this paper. We consider that

existing

^{data do not}

allow yet any definite

prediction.

^This

subject

^is

treated in theoretical papers e.g. references

[8-16].

The energy

dependence

of np

scattering amplitudes

and of the ratio of the real to

imaginary

part ^{of the}

spin independent

^forward

scattering amplitude

^is

discussed in section 5. Section 6 is devoted to a

discussion of

polarized

^neutron beams. Our conclu- sions are summarized in the final section 7.

2. Symmetries ⁱⁿ neutron-proton scattering.

2.1 TIME REVERSAL INVARIANCE. ^- Tests of time reversal invariance

(TRI)

ⁱⁿ nucleon-nucleon scatter-

ing

^have recently ^been discussed in considerable detail

[6].

^The np => np

scattering

^{matrix was writ-}

ten in terms of the 8

complex amplitudes a (T, 9 ), ..., h (T, 0 )

^as

where

and ki ^and k f ^{are unit vectors in} the direction of the incident and scattered

particles

in the CM. In the

laboratory

system ^{we shall use unit vectors in the} directions of the incident, scattered and recoil _par- ticle.momenta

together

^{with the} transverse vectors

(see Fig. 1

^{of Ref.}

[4]).

The

scattering

^matrix

(2.1)

is Lorentz invariant

(invariant

under rotations in the

c.m.s.)

^and

parity

invariant. For identical

particles (e.g.

pp

scattering

or np

scattering

^{under the}

assumption

^of

isotopic

spin invariance)

^{we have :}

Time reversal invariance

implies

The

simplest

^{test of TRI is the}

only

^{one that has}

been

performed

^{in pn}

scattering, namely

^{the «}

polari-

zation

equals

asymmetry ^{» test :}

where a ⁼

do- ₍₀₎

is the

unpolarized

differential dQ

cross section and the stars denote

complex

^con-

jugation.

^{It would be}

highly

^{desirable to}

disentangle

the TRI

violating amplitudes

g ^and h, ^{i.e. to}

perform

the two tests in

(2.5).

They ^{should be}

performed

ⁱⁿ

regions,

^{where the}

amplitudes

^{c and d are known to}

be

large,

^{i.e. in}

regions

^{where the}

quantities :

are all

large.

^{Note that the}

amplitude

^{h would not}

manifest itself in pp

scattering,

^{because of the Pauli}

principle.

Eleven other types ^{of TRI tests} in np

scattering, involving.

^two component

polarization

^{tensors :}

Dpoqo, Dopoq, Kpooq, Kopqo’ Aoopq

^and

C pqoo

are

analysed

^{in reference}

[6].

^None of them has so

far been

performed.

It should be mentioned that TRI violations in nucleon-nucleon

scattering

^{have been}

predicted

ⁱⁿ

specific

^models

[17, 18].

^A

surprisingly

large ^TRI

violation in inelastic nucleon-nucleus reactions has been

reported

^{in reference}

[19] ;

it still needs to be confirmed.

Analysing

power and

polarization

^{data are dis-}

cussed below in section 4.

Unfortunately

they ^can

usually

^{not be used for TRI tests} since the data are

already presented

^{in an}

averaged

^{form where the}

P ⁼ A

equality

^is

imposed.

^Three

exceptions

^are presented ⁱⁿ

figure

1, ^where the black

symbols

represent ^the

analysing

power Aoo,,o ^or

Aooon, all

empty symbols ^{denote the}

polarization P nooo or

Powxr ^The precision ^{of these} measurements is insuffi- cient to determine a

possible

^TRI violation. In

particular

^{in the}

Saclay-Geneva

PSA, ^{all these data}

were introduced as an identical

quantity,

^{and show}

similar

X 2

contribution. A further TRI test was

performed

^{at LAMPF}

[20]

comparing

at 775 MeV and Ocm ^{= 133* to}

Po. = -

^{0.200 ±}

0.017 at 800 MeV and ocm ^{=133 ° in}

quasi-free

pn

scattering.

^{No visible P A} difference was observed in any of the above ^cases.

It would however be important ^to

perform

^accu-

rate simultaneous P-A experiments for different

energies

^and

angles

^to

verify

^{that both}

amplitudes g (T, 0 )

^and

h (T, 8 )

^{are indeed}

systematically equal

to zero.

2.2 ISOSPIN INVARIANCE IN ELASTIC np => np ^SCAT- TERING. ^- To test

isospin

invariance in the _np system we assume TRI and put g ^{= h = 0 in}

Fig. ^{1. -} Comparison ^of analysing power data Aoono ^and A.,, (black symbols) ^with polarization ^data P 0000 ^and Ponoo (empty symbols). ^The points ^{referred to as 80/N-39}

are A.,,, 67/C-13 and 64/D-7 are Aoono, ^{71/L-14 are} P 0n00’ ^67/K-8, 70/B-7 and 76/Z-16 are P 0000. ^{The measure-}

ments 80/N-39 and 71/L-14 were performed ^{with free}

neutrons, all others with ^a deuterium target.

equation (2.1).

^The

isospin violating amplitude

ⁱⁿ

(2.1)

^is

f (T, 6). Experiments

^that will detect the presence of the

amplitude f(T, 6)

^were discussed in detail in reference

[21].

^The

simplest

^{one is}

measuring

^the difference between the asymmetry ⁱⁿ

the

scattering

^of

polarized

^{neutrons on}

unpolarized

protons ^{and in the}

scattering

^of

unpolarized

^neutrons

on

polarized

protons. ^{Four other tests of}

isospin

invariance

involving

^two component

polarization

tensors exist. They ^are

given

by the relations :

Here 0, 61

and 0 2

^{are the c. m. s.}

scattering angle,

^the

laboratory scattering angle

^{and the}

laboratory

^recoil

angle, respectively (in

^the nonrelativistic limit we

have 01=

0/2,

02=

(1T - o ) /2).

The

amplitude f

^{can be}

split

^{into two} parts :

where

fi

contains « noncontroversial » electro-

magnetic

contributions. The

amplitude f 2

^contains

contributions from

genuine isospin violating

strong interactions

(if they exist),

but also from indirect

electromagnetic

interactions effective

only

^{in the}

presence of strong interactions

(e.g.

^{due to radiative}

corrections to nucleon-meson vertex

functions).

^The

definition of

f i

^{is of course}

quite subjective

^{and a}

variety

of different calculations of

fi

^is

given

^{in the}

literature

[21-25].

^The

amplitude

^of

physical

^interest

is

mainly f 2

^and is best measured away from the forward Coulomb

peak.

Furthermore,

experiments specified

ⁱⁿ

equations (2.7)

^to

(2.11)

^{should be}

performed

ⁱⁿ energy and

angular regions

^{where the}

corresponding

^invariant

amplitude

^{a, b, c, d, or e,}

interfering

^with

f,

^is

large. E.g. experiments

^re-

quired

ⁱⁿ

equations (2.8)

^and

(2.9)

should be per- formed where :

and

are

respectively,

^{known to be}

large.

At least in

principle,

each of the

isospin

^invariance

tests

given

ⁱⁿ

equations (2.7)-(2.9)

^{can be}

performed

in a

single experiment using

^{one and the same}

experimental ^set up. So far, ^{this has not been}

performed.

The

only

^{relation that can at this} stage be tested is

given

ⁱⁿ

equation (2.7) (note

that both

Aown

^and

Aoono

^can be obtained as

by-products

^{in measure-}

ments of

Aoonn).

Below 100 MeV both

analysing

powers ^are very small and all

comparisons

^are

inconclusive.

A

specific

apparatus ^was

recently

constructed at TRIUMF

[26]

^{in order to test the}

isospin

invariance.

At 477 MeV the authors

[27]

^{measured the}

angle

where the observables

Aoono

^and

Aooon

^{cross the zero}

value

(crossover point).

^This type ^of

experiment

^is

more

precise

^{since the}

slope

^of

is very steep and known from

existing

^PSA

predic-

tions. The

experimental

difference in the zero cros-

sing angles of Aoono

^and

A.,,

^as determined from the neutron

laboratory scattering angles

00 n ^is

The

analysis

^{in terms of the} proton

laboratory scattering angles 80 p ^yields

The difference in

analysing

power ^was deduced from these results

using

^the

slope

values from PSA of reference

[3].

^This

gives

The

slopes

^{from the}

Saclay-Geneva

^PSA

[2]

^are

approximately

^{3 %} steeper than those from Arndt

et al.

[3]

^{which has little influence on} the results. The

quoted systematic uncertainty, given

ⁱⁿ

parentheses,

is the worse estimate at the present stage ^{of the}

analysis.

The theoretical

predictions [28]

^{for the}

crossover

angle

^is

Similar measurement will be undertaken

by

^the

same group ^at 350 MeV, where the authors will increase the

precision

^{to ± 8 x 10- 4.} Note that the

predictions [28]

^are

practically

^{the same at this}

energy.

3. Neutron proton scattering ⁱⁿ particular situations.

Before

discussing

^the

experimental

^status of np

scattering

^{and the}

possible

reconstruction of np ==> np

scattering amplitudes

^{we shall}

briefly

^dis-

cuss situations in which

only

^a smaller number of

amplitudes

^{survives. We make use of our}

previous

articles on the nucleon-nucleon

scattering

^formalism

[4-6, 29]

^to derive formulae for

experimental

^quan-

tities for

scattering

^at

specific angles (0

^{= 0, ir and}

7T/2)

^{or at} threshold energy.

For forward and backward

scattering

the nucleon- nucleon

scattering

^{matrix must be} invariant with respect ^to rotations about the direction of the beam.

Hence, ⁱⁿ

equation (2.1)

^{we have :}

and also

and

respectively.

^For

helicity amplitudes Oi

^this

implies :

and

respectively (for

^{relevant notations see re-}

ferences

[4-7]).

^The

singlet-triplet scattering

^matrix

is

diagonal

^{for 0=0 and o = ’IT, so that the}

only surviving

^{terms are :}

where 0 a

^{= 0 or 7r.}

Only

⁹

experimental quantities

are

linearly independent

^{at these}

angles (and

⁴

nonlinear relations exist between

them).

^{Tables III}

and V of reference

[4] greatly simplify

^{in these two}

cases. For forward and backward

scattering

^we

have :

and

respectively.

^{The behaviour of all} np => np ^lab.

experimental quantities

^{at these}

angles

^{is sum-}

marized in tables I and II.

At T ⁼ 0

(elastic threshold)

^the

scattering

^matrix

equation (2.1)

^is

independent

^{of the momenta}

(S

wave

scattering only)

and reduces to :

i. e. we have :

Only

^four

experimental quantities

^{are nontrivial}

and

linearly independent

^{at T =} 0 ; they ^{are listed in}

table III. The situation at threshold is

particularly simple

^{in the center of mass} system ^{where we have :}

where 8 n ^is the Kronecker delta, Erst is ^a

completely antisymmetric

^tensor

satisfying :

(with

^{I, m and n as in}

(2.2).

The labels _{p, q,} r and t

run

through

I, ^{m and} n, the labels a, B

through

^{I and}

n).

Exactly ^{at threshold the}

laboratory

system is, strictly

speaking,

^{not defined, nor are the}

angles

0, 61 ^and 62. The formulas of table III,

giving

^the

threshold behaviour of

experimental quantities

ⁱⁿ

the

laboratory

system, ^{are to be}

interpreted

^as limits, ^{valid when}

equation (3.7)

^{holds, but the}

momenta of the

particles

^{involved are}

sufficiently large

^to define the directions k, k’, k" and the

scattering angles satisfying

This is the case e.g. for the scattering ^{of thermal}

neutrons on protons.

Assuming

isospin invariance and

ignoring

^elec-

tromagnetic

interactions we can relate some np

scattering quantities

^{at 0 =}

7r /2

^{to the}

correspond-

Table I. ^-

Experimental

quantities ^at

OCM

^{= 0° in terms}

of helicity amplitudes 03A61

^to

03A65*

ing

pp

quantities.

^More

specifically

^{we have}

[4] :

The relations

(3.11)

^{hold at :}

where a ⁼

8 -

_{2 0 1 is the}

_angle

_of relativistic

spin

rotation

[4].

The nucleon-nucleon amplitude reconstruction is

greatly simplified

^{for 0 =} 0, (J ^{= iT or T = 0. Indeed}

using

^{tables I and II we find} that for forward and backward

scattering

^the

helicity amplitudes

^{can be}

reconstructed with no

ambiguity (neither

^continuous

nor

discrete),

except ^{for one overall}

phase,

^from

6

experiments.

^{These can be chosen to involve}

only

one final state

polarization,

e.g. that of the scattered

particle.

Let us use the overall

phase ambiguity

^{to choose}

the

helicity amplitude 01

^{to be real and}

positive.

Table II. ^-

Experimental

quantities ^at

°CM

^{= 1800 in terms}

of

helicity

amplitudes 03A6’1

^to

03A65.

For 0 ⁼ 0 one

possible

reconstruction is :

Four nonlinear relations exist between the nine

linearly independent experimental quantities.

They

can be chosen to be :

Table III. ^-

Experimental

quantities ^at

T kin

^{= 0 in terms}

of amplitudes

^{a, b, c,} d, ^e.

A

possible

reconstruction for 0 = 7r is

given by :

Nonlinear relations similar to

(3.13)

^can

easily

^be

derived for 0 ^{= 7r.}

At threshold it is easiest to reconstruct the in- variant

amplitudes, choosing a

^{to be real and}

posi-

tive. We have:

At threshold we also have :

For a discussion on np

amplitude

reconstruction at

arbitrary energies

^and

angles

^{see reference}

[30].

4. Main features of the n-p experimental quantities.

All discussed

experimental quantities

^{are to be}

found either in reference

[7]

^{or in table II of refer-}

ence

[2].

We stress that no new

spin dependent

^{data on} np

scattering

ⁱⁿ the energy

region

^{70-200 MeV have}

been

published

since 1968. Hence _many of the

experimental

np

quantities

^are

poorly

measured in this

region.

Moreover, earlier data are

grouped

around the _energy 140 MeV. We do not attach a

great

physical significance

^to the behaviour of the

predicted

observables in this energy

region.

The corridor of ^« errors » shown in some

figures

was calculated from the square ^{roots of} the

diagonal

elements of the matrix. It is much narrower than the

error

corresponding

^{to the «} confidence level 1 a >>.

The

meaning

of the indicated corridor is that it indicates the

regions

^{in which further} measurements would be

particularly

^fruitfull.

4.1 UNPOLARIZED TOTAL CROSS-SECTION UOtot. ^- The _np total cross section has been measured

starting

^from the kinetic energy ¹ eV. The total cross

section is found to be constant up ^{to -} 200 eV then

°

decreases up ^to 400 MeV. The

generally accepted

value at zero kinetic energy has been ^most

precisely

measured in

[31]

^{and is}

corresponding

^to the np

scattering length as (np ) _

- 23.749 ± 0.009 Fermi.

In the

region

0.74-33 MeV there exist 800

points

measured at the Karlsruhe isochronous

cyclotron [69/C-89].

^These

points

^{have a}

typical

^{relative error}

of 1 % and define

completely

the energy

dependence

of

U 0 tot in

^this

region.

^In the energy range 88- 151 MeV the energy

dependence

^of UOtot ^was first determined

by

^the

precise

measurement carried out at the Harvard

synchrocyclotron [66/M-3].

^Other

existing

^data

[7]

^{are also in} agreement ^with

[66/M-3].

The energy

dependence

^of U 0 tot in the energy range 10-170 MeV are shown in

figure

^{2a. The curve is the}

phase

^shift

analysis (PSA) prediction [2],

^{that of}

Arndt et al.

[3]

^{is not shown as} it is in

perfect

agreement.

Representative

^{measured data}

points [66/M-3,

^31,

32]

^{as well as few}

points

^{from re-}

ference

[69/C-89]

^{are also}

plotted.

Above 140 MeV the _UOtot ⁼

f (T)

is illustrated in

figure

^{2b. A} considerable

disagreement (up

^{to 2 mb}

at 400

MeV)

is observed in the energy

dependence

between LAMPF

[32]

^{and SIN}

[33]

^{data on one}

hand and TRIUMF

[34]

^{and PPA}

[73/D-109]

^{data on}

the other. At

energies

^{above 650} MeV the PPA

points

^{and LAMPF data} again agree but both sets

disagree

^with the RHEL pn

quasielastic

^re-

sults

[66/B-26].

^{The Dubna data}

[55/D-ll]

^{as well as}

other

existing points [7]

^cannot

help

^{to draw} any conclusions due to their large ^errors. The fact that the recent SIN data

[33]

^{have confirmed the} energy

dependence

^{observed at LAMPF}

[32]

^{and that both}

of these data are fitted without _any normalization in the phase ^shift analyses ^of references

[2, 3] give

definite credence to these two sets of data.

Figure

2c shows the

isospin

^{I = 0} part ^{of the total}

cross section.

4.2 POLARIZED TOTAL CROSS SECTIONS. ^- The total cross section for both initial

particles polarized

is

given

by :

where PB ^and PT ^{are the beam and} target

polarization

vectors,

respectively,

^{and k is a unit vector in the}

beam direction. The differences åUT ^and

åUL

^are

related to the contributions _{a, to,} and _{U 2 tot}

by :

The

quantities

åUT ^and AOL ^were

recently

^measured

at Satume II at 630, 880, 980 and 1 080 MeV

using

the

polarized

^{neutron beam and the}

Saclay

^frozen

spin polarized

proton target. ^The

experimental

^set-

up ^and

preliminary

^{results are}

given

^{in references}

[35, 36].

^Five åUL

points

^were derived from the

Argonne-ZGS ACrL(pp) and åUL(pd)

^data

[37]

corrected for the three

body

interactions

[38].

^Pre-

dictions from the PSA

[2, 3] (presented

^{as full and}

dashed-dotted line,

respectively)

^for Ul tot ^at low

energies ^{are shown in}

figure

3a and those in the energy range 90-850 ^{MeV in}

figure

^3b.

Figures

^{3c, d}

show the I =

0 part of U 1 tot

^{at low and}

higher energies, respectively.

^In

figures

4a, b, c, d are

given corresponding predictions

for the total cross section difference - AUL.

Existing

^{data are also}

plotted.

Both PSA

[2, 3] give

similar results for _{Ul tot} up ^to 700 MeV

(Fig.

^3a,

b)

and agree with the

Saclay point

at 630 MeV. The other’

Saclay

^data

[36]

suggest above 800 MeV a behaviour indicated in refer-

ence

[3].

^The

predictions

^{for -}

AaL (Fig. 4a, b)

differ over most of the energy range

[50-800 MeV].

The

existing

^data

on åu L (pd) - AaL(pp)

^{are intro-}

duced in the

Saclay-Geneva

PSA, ^{but were not used}

in reference

[3].

^{The new}

Saclay

^data

disagree

^with

the corrected

AaL(pd) - AAL(PP) points [38]

^and

confirm the prediction ^of Arndt et al.

[3].

4.3 TOTAL INELASTIC CROSS SECTION. ^- A com-

plete

discussion of this

analysis

^is

given

^{in refer-}

ence

[39]

^{but an}

updated

paper is under

publication.

The total inelastic cross section

(called

^{also « reac-}

tion cross section

»)

^{cannot be}

directly

^{measured. It}

can however be determined as a sum of

integrated

total cross sections for all inelastic channels. It can

also be determined as the difference between the total cross section for all reactions and the total elastic cross section :

(both quantities

^{on the}

right

^{hand side can be}

measured

simultaneously

in bubble chamber ex-

periments).

In the energy range below 800 MeV

only

^four

different

channels contribute

(1)

np ==> 7T ° d,

(2)

np ==> np7T °,

(3)

np ==> pp7T - ^and

(4 )

np ==>

nn7T +. The two pion

production

^is

negligible.

Reaction

(1)

^{was measured for np} scattering ^but

was

always

normalized to

U tot (pp

=> 7T +

d )/2

^as-

suming isospin

invariance.

Consequently

^{no check of}