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Author: Daniel Fernández Ruiz

Supervisors: Dr. Olof Tengblad, Dra. MJG Borge Experimental Nuclear Physics Group (IEM-CSIC)

Consistency tests of the decay of with the R- Matrix formalism

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Daniel Fernández Ruiz R-Matrix analysis (1/11)

Motivation

The decay of is of interest for both astrophysics and nuclear structure

Nuclear Strucutre

Astrophysics

 Part of the stellar hydrogen-burning chain

 Source of high-energy solar neutrinos above 2 MeV

Main contributor to what was known as the “solar neutrino problem”

 Through the decay of

⁸

B we study the structure of

⁸

Be

The 16.6 and 16.9 MeV levels of

⁸

Be are assumed to form a fully

mixedisospin doublet

(Only known case of Nuclear Chart)

We can experimentally check this assumption!

Our objective is to determine the mixture coefficients of the isospin doublet

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IS633

Experiment IS633 was conducted at CERN- ISOLDE in 2017 to study the structure of

⁸

Be

Technique

I. nucleus is implanted in a foil

II. The decay of populates states of III. has an – break up

IV. Construction – coincidence spectrum through a system of four telescopes

Schematic

Result: – coincidence spectrum

PAD DSSD

I II

IV IV

III

Telescope

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R-Matrix formalism  Nuclear resonances in reaction studies  β-decay followed by 2-body break up

A.M. Lane et al., Rev. Mod. Phys. 30(2):257-353, 1958 F.C. Barker, Aus. Journ. Phys. 22(3):293-316, 1969

Ingredients: α-α coincidence spectrum + coincidence response matrix + fitting range Method: The R-matrix parameters are selected to fit the experimental data ( minimization )

S. Viñals used the R-Matrix formalism to study the 16 MeV isospin doublet

 Restrict the range of our fitting to the región of interest

 Good fit to the experimental data

× Not take into account the effect of the 3 MeV level

 Better values for the

× Requires modifying the error bars

 Start by fitting the doublet region 2

⁺

doublet approach

Holistic approach

 Expand the fitting range to include the 3 MeV level

Pervious analysis

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The R-Matrix parameters allow us to study the Isospin mixing through two methods

Method 1

Method 2

Completely mixed in isospin

Doublet

Pervious results

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We have performed two types of cross-checks to find the reason for this discrepancy

So, that’s all?

Not yet, we would like to know why there is a discrepancy between the Decay Width () obtained through our R-Matrix and those of the standard literature [Tilley (2004)]

Consistency tests of S. Viñals results

(PART I)

Comparison with previous results

(PART II)

Tilley (2004)

Daniel Fernández Ruiz R-Matrix analysis (5/11)

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Results JYF08

Levels Parameters Literature [Til04] S.Viñals Check I Check II Check III

(fm) 1.35 1.35 1.35 1.35 1.35

(2-17.2

MeV)

14.4 3991

14.3 12.0

E (keV) 3030(10) 3058(31) 2959.3 3050.75 3036.9

(keV) 1513(15) 1876(94) 1415.7 1949.8 1883.1

E (keV) 16626(3) 16632(83) 16616 16627 16623

(keV) 108.1(5) 129.47(28) 180 123.98 114.67

E (keV) 16922 16921(85) 16919 16917 16913

(keV) 74.0(4) 112.5 74.076 99.735 99.179

E (keV) 21205 17238 23338 37000

(keV) 119.11 104.26 1331.4 12116

1.35 1.35 1.35 1.35 1.35

14.4 3991

14.3 12.0

E (keV) 3030(10) 3058(31) 2959.3 3050.75 3036.9 1513(15) 1876(94) 1415.7 1949.8 1883.1

E (keV) 16626(3) 16632(83) 16616 16627 16623

108.1(5) 129.47(28) 180 123.98 114.67

E (keV) 16922 16921(85) 16919 16917 16913

74.0(4) 112.5 74.076 99.735 99.179

E (keV) 21205 17238 23338 37000

119.11 104.26 1331.4 12116

Check I: =Lit (fix)

Check II: =Lit (not fix) Check III:

 : Lowest values; larger value of the BKG.

 =Lit (fix): Fixing does not generate good results.

 =Lit (not fix) : improvede fit, results closer to those S- Viñals

To test the consistency of our results we repeated the fit under certain constraints

Daniel Fernández Ruiz Part I: Cross-checks R-Matrix analysis (6/11)

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Results JYF08

Levels Parameters Literature [Til04] S.Viñals Check I Check II Check III

(fm) 1.35 1.35 1.35 1.35 1.35

(2-17.2

MeV)

14.4 3991

14.3 12.0

E (keV) 3030(10) 3058(31) 2959.3 3050.75 3036.9

(keV) 1513(15) 1876(94) 1415.7 1949.8 1883.1

E (keV) 16626(3) 16632(83) 16616 16627 16623

(keV) 108.1(5) 129.47(28) 180 123.98 114.67

E (keV) 16922 16921(85) 16919 16917 16913

(keV) 74.0(4) 112.5 74.076 99.735 99.179

E (keV) 21205 17238 23338 37000

(keV) 119.11 104.26 1331.4 12116

1.35 1.35 1.35 1.35 1.35

14.4 3991

14.3 12.0

E (keV) 3030(10) 3058(31) 2959.3 3050.75 3036.9 1513(15) 1876(94) 1415.7 1949.8 1883.1

E (keV) 16626(3) 16632(83) 16616 16627 16623

108.1(5) 129.47(28) 180 123.98 114.67

E (keV) 16922 16921(85) 16919 16917 16913

74.0(4) 112.5 74.076 99.735 99.179

E (keV) 21205 17238 23338 37000

119.11 104.26 1331.4 12116

Check I: =Lit (fix)

Check II: =Lit (not fix) Check III:

 : Lowest values; larger value of the BKG.

 =Lit (fix): Fixing does not generate good results.

 =Lit (not fix) : improvede fit, results closer to those S- Viñals

To test the consistency of our results we repeated the fit under certain constraints

Daniel Fernández Ruiz Part I: Cross-checks R-Matrix analysis (6/11)

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We will use the data of this experiment as a reference to compare with our data

Levels Parameters Literature

[Tea04] JYFL08

(fm) 1.35 1.35

(2-17.2 MeV) 0,97

E (keV) 3030(10) 3054

0.011813(56) 0.01020

(keV) 1513(15) 1472

E (keV) 16626(3) 16544

- -

(keV) 108.1(5) 355

E (keV) 16922 16887

- -

(keV) 74.0(4) 120

E (keV) 21000

0.032

(keV) 176

Levels Parameters Literature

[Tea04] JYFL08

1.35 1.35

0,97

E (keV) 3030(10) 3054

0.011813(56) 0.01020

1513(15) 1472

E (keV) 16626(3) 16544

- -

108.1(5) 355

E (keV) 16922 16887

- -

74.0(4) 120

E (keV) 21000

0.032 176

Daniel Fernández Ruiz Part II: Comparison with JYFL08 R- Matrix analysis (7/11)

JYFL08 was an experiment conducted in Finland in 2008 ,it served as the basis of O.Kirsebom's PhD thesis

Before IS633 it was the best experiment of this type

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 Comparasion of -coincidence data of JYFL08 and IS633 (- window: 200 keV)

 Green= raw - coincidnece (IS633);

 Purple=- coincidnece (IS633) corrected for loses on the Carbon foil;

 Blue= raw - coincidnece (JYFL08);

 The 16,9 MeV level isn´t resolved by JYF08

 IS633 resolves the 16,9 MeV level due to its higher stadistis.

 Statistical difference between data sets determined through their coefficient.

 A linear fit to the most stable región to determine the proportionality constant.

We will compare the 3 MeV region

Daniel Fernández Ruiz Data comparison R- Matrix analysis (8/11)

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Linear Scale

Normalizing the data of experiment IS633 to JYFL08 we can better compare them

Data set - coincidence - coincidence + catcher JYL08 Centroid 2930 keV

IS366 Centroid 2910 keV 2930 keV

Diff (JYL08-IS366) 20 keV 0 keV

Data set

JYL08 Centroid 2930 keV IS366 Centroid

Diff (JYL08-IS366)

However, we still need additional checks

The maximum of our data sets aligns well with the JYFL08

Daniel Fernández Ruiz Normalized Data comparison (Linear) R-Matrix analysis (9/11)

Normalized IS633 data exhibits a similar form to JYFL08.

We first compare their

centroids of the distirbutions

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Log Scale

Results indicate that the curves we obtained are really similar to experiment JYFL08

b

A way to evaluate the similarities between data sets is to use a residue function

The residue function (fig b) is almost zero for the low energy region but increases for high energies

Zooming into the low energy region (fig c) we observe that the residue function stable around 0

Daniel Fernández Ruiz Normalized Data comparison (log) R-Matrix analysis (10/11)

a

c

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Daniel Fernández Ruiz R-Matrix analysis (11/11)

Part I

 Experiment IS633 is the first experiment that enabled us to study thedoublet of

 The R-matrix formalism enables us to study the 16 MeV isospin doublet of

 We performed cross-checks to compare our results with the literature

 The best fits are produced by fixing the background energy to 37 MeV

Thank you for your attention

Part II

 We have compared our data with experiment JYFL08.

 The comparison of our normalized data with JYFL08 indicates that IS633 is consistent with previous results.

 We are still studying why we do not reproduce the values of the 3 MeV level with R- matrix

Closing remarks

Next steps

 Repeat or fits with a different number of levels (2 Backgrounds)