This work was supported by the U.S. DOE Office of Science under Grant No. DEFG02-88ER-40404

Romualdo deSouza, TAMU-Commerce, Feb. 5, 2015

Indiana University: T. Steinbach, M.J. Rudolph, Z.Q. Gosser, K. Brown✼, J. Vadas, V. Singh, S. Hudan, RdS Florida State: I. Wiedenhover, L. Baby,S. Kuvin Vanderbilt University: S. Umar, V. Oberacker

Overcoming Barriers to Forge Elements in the Dark

How ever are we going to get to the other side?

• Fundamentals of supernova explosions are not understood! • Synthesis of the heavy elements is not understood • Limits of nuclear stability (superheavy elements, N/Z exotic) poorly known

Only elements Z=1-4 produced in the Big Bang

Chemical diversity We know the composition of stars based on their light (atomic emission lines)

H burning 4 p 4He + 2β+ + 2ν

He burning 3 4He 12C 4 4He 16O

12C/16O burning Mg, Na,

Si burning Up to 56Fe

Big Bang 13±1Gy T,ρ HI

Expansion: T,ρ drop H,He,Li,Be formed (3 min.)

Inhomogeneities aggregation T,ρ ↑

T, ρ increase

Supernova explosion Synthesis of

elements beyond Fe (r process)

Ejecta repopulates interstellar medium enriched with heavy elements

Remnant core: Neutron star

M>10Msun

Making elements : The Coulomb barrier problem

(Z1,A1) (Z2,A2) (Z1+Z2,A1+A2)

The two nuclei are charged and repel each other unless they are very close (touching)

rZZrV 21)( ∝Coulomb’s Law:

The two nuclei have to overcome the Coulomb repulsion (barrier) in order to experience the attraction of the strong nuclear force which is short range.

Overcoming barriers

What if the two nuclei do not possess sufficient energy to overcome the barrier ?

• Particle can tunnel (exist in classically forbidden region) and emerge on other side. SENSITIVE TO WIDTH OF BARRIER

• Effect of barrier is observed even if E > U

Measuring the fusion cross-section is therefore intrinsically related to measuring the detailed shape of the fusion barrier (a dynamic quantity as the nuclei approach)

Oakridge National Laboratory TAMU

Cyclotron Facility I.U. Cyclotron Facility

GANIL, France GSI, Germany

NSCL (FRIB) Michigan State Univ. Argonne

National Lab.

To overcome this Coulomb repulsion one has to provide kinetic energy to the nuclei. This can be done by: a) Raising the temperature (e.g. stars, tokamaks) b) Using an accelerator

The Chart of the Nuclides and Terra Incognita

Radioactive beam facilities allow one to produce neutron-rich nuclei along the r-process path.

Neutrons

Prot

ons

Stable Nuclei

Known Nuclei

Terra Incognita

Neutron stars represent an extreme point on this diagram

Fusion reactions in the outer crust are responsible for the X-ray bursts and superbursts

Problem: At the temperature of the crust, the Coulomb barrier is too high for thermonuclear fusion of carbon – another heat source is needed.

X-ray bursters and Superbursters

More energy release in one superburst than one decade from our sun!

Rossi Explorer satellite 1995-2012

The crust of an accreting neutron star is a unique environment for nuclear reactions

Atmosphere: Accreted H/He

Ocean:

heavy elements

Crust

Carbon + heavy elements

Density depth

~105 g/cm3

5 m

~109 g/cm3

30 m

~1010 g/cm3

100 m

Outer crust of an accreting neutron star

Structure of an accreting neutron star crust

Fusion of Neutron-rich Light Nuclei One potential heat source, proposed (Horowitz et al.) to heat the crust of neutron stars and allow 12C fusion, is the fusion of neutron-rich light nuclei (ex. 24O + 24O) -- More recently mid-mass nuclei have been suggested.

24O + 24O Fusion: If valence neutrons are loosely coupled to the core, then polarization can result and fusion enhancement will occur

24O is currently inaccessible for reaction studies

Instead study other neutron rich isotopes of oxygen (18,19,20)O on 12C (19,20O are radioactive)

16O Core

16O Core

valence neutrons Horowitz et al., Phys. Rev. C 77, 045807 (2008)

Umar et al., Phys. Rev. C 85, 055801 (2012)

R.T. deSouza, S. Hudan, V.E. Oberacker, S. Umar Phys. Rev. C88 014602 (2013)

Density constrained TDHF calculations • Damped dipole oscillation and presence of surface waves clearly visible.

• Fusion events and deeply inelastic events dominate at these near barrier energies

• Fusion is distinguished from deeply inelastic collisions by the existence of a single heavy nucleus after the collision

Quantum mechanical calculations can also be performed to investigate the fusion process

1) Nuclear astrophysics: Nuclear reactions in outer crust of a neutron star

2) Nuclear physics: dynamics of fusing two neutron-rich nuclei

Motivation

24O + 24O not possible

Measure fusion in 16,18,19,20O + 12C

19O and 20O are radioactive beams!

Challenge: Radioactive beams are/will be available at intensities of ~103 – 105 ions/sec– a million times less intensity than previously used in fusion studies.

When comparing 18O + 12C to 16O + 12C DC-TDHF predicts a larger increase as compared to the experimental data.

What happens (in reality) to the fusion cross-section as the oxygen nucleus becomes increasingly neutron-rich?

Systematic fusion data to address this question is necessary!

Fusion of neutron-rich radioactive beams with light targets

20O + 12C 32Si* (E* ~ 50 MeV)

Romualdo deSouza, ACS, Indianapolis 2013

32Si* 29Si + 3n 32Si* 29Al + p + 2n 32Si* 26Mg + α + 2n

Charged particle channels

Neutron only channel

Evaporation residues

First stage (described by TDHF):

Second stage (described by statistical model):

100 feet

SPIRAL@GANIL

Good cheese, cider, and an accelerator facility with excellent technical support ISOL technique Primary beam: Ar Production target: C(graphite) CIME reacceleration: ~10 MHz 20O2+ t1/2 : 13 s

A “simple” counting experiment

Measure the number of beam particles by counting them individually

beam

fusionfusion N

Nk=σ

Count the number of residues Reciprocal of target thickness

Experimental Setup

Incident Beam: 20,19,18,16O + 12C @ 3 MeV/A Intensity of 20O: 1-2x104 pps Degrader ion chamber (CF4) reduces energy to1-2 MeV/A and identifies particle (ΔE) Target: 100 µg/cm2 carbon foil (0.45 nm) T2: θLab = 3.5 - 10.8°; T3: θLab = 11.3 - 21.8° Time-of-Flight (TOF) between target-MCP and Si (T2, T3)

Active Collimator

20O BEAM

Degrader Ion Chamber

SBD

1st Timing Detector and target

2nd Timing Detector

T3 T2 Zero Degree Ion

Chamber

ΔE1 ….. ΔE5 ΔE1 ….. ΔE6

This image cannot currently be displayed.

M.J. Rudolph et al., PRC85, 024605 (2012).

M.J. Rudolph et al., Phys. Rev. C85, 024605 (2012).

total

Associated with CP emission

• Is the total fusion cross-section larger than predicted? (First stage underpredicted) • Is just the part of the fusion cross-section associated with charged particles larger

than predicted? (Second/de-excitation stage incorrect)

Our initial experiment to measure σfusion for 20O + 12C failed…BUT we did learn something interesting!

Gridless MCP Detector Minimize extraneous material in the beam path

Crossed electric and magnetic field transports electrons from secondary emission foil to the microchannel plate (MCP)

20 neodymium permanent magnets produce magnetic field (~85 gauss)

6 grid plates produce electric field (~101,000 V/m)

C foil frame biased to -1000 V MCP with 18 mm diameter Time resolution (MCP-MCP) ~ 350 ps

Beam

B E

Bowman et al., Nucl. Inst. and Meth. 148, 503 (1978) Steinbach et al., Nucl. Inst. and Meth. A 743, 5 (2014)

What do we want to measure?

Excited nucleus decays:

To measure the fusion cross-section we need to count the number of evaporation residues relative to the number of incident O nuclei

Emission of evaporated particles kicks evaporation residues off of zero degrees

Target Beam

Evap. Residue

Evaporation residues Evaporated particles

Method for Identifying Evaporation Residues

Stop time Energy

Start time

Beam Residue

To distinguish fusion residues from beam particles, one needs to measure: Energy of the particle Time of flight of the particle

18O beam was provided by the Tandem van de Graaf accelerator at Florida State University (Feb. 2014)

18O @ Elab = 16 – 36 MeV IBeam ~ 1 - 4.5x105 p/s Wiedenhover et al., (5th Int. Conf. on Fission & Prop. of Neutron-rich Nuclei, 2012)

www.physics.fsu.edu/Nuclear/Brochures/SuperconductingLinearAcceleratorLaboratory/default.htm

18O + 12C Measurement at Florida State U.

Time-of-flight of beam measured between US and Tgt gridless MCP detector

Elastically scattered beam particles and evaporation residues: Time of flight measured between Tgt MCP and Si detectors Energy measured in annular Si detectors (T2, T3)

18O BEAM

US MCP Detector

Tgt MCP Detector

T2

~ 130 cm ~ 13 cm

PMT

T3 LCP Det.

Array

7 CsI(Tl)/photodiode detectors used to measure light charged particles

PMT (coupled to plastic scintillator) measures zero degree beam particles

Si Detector New design (S5) from Micron Semiconductor

Single crystal of n-type Si ~ 300 μm thick Detector acts as a reverse biased diode

Segmented to provide angular resolution

Used to give both energy and time information S5 (T2) Si Design

Pies 16

Rings 6 24 ring segments Inter-strip width 50 μm Entrance widow

thickness 0.1-0.2 μm www.micronsemiconductor.co.uk

Steinbach et al., Nucl. Inst. and Meth. A 743, 5 (2014) deSouza et. al., Nucl. Inst. and Meth. A 632, 133 (2011)

Fast timing electronics gives timing resolution of ~ 450 ps

(Need ~ 1 ns time resolution)

Identifying Evaporation Residues 18O + 12C @ ELab = 36 MeV

Rudolph et al., Phys. Rev. C 85, 024605 (2012) Rudolph, Master’s Thesis, IU, 2012

• Evaporation residues are clearly identified from Elastic scattering and beam scatter particles

• Alpha particles are also clearly distinguished

18O + 12C Fusion Excitation Function

Measured the cross section for ECM ~ 6 – 14 MeV

Good agreement with existing data

However we extend the measured cross-section to approx. the 2 mb level (one order of magnitude lower than previously measured and with a million times less in beam intensity!)

18O + 12C Excitation Function: Comparison with DC-TDHF

Progress on the theoretical front as well…

But even with inclusion of pairing the theoretical excitation function has the wrong SHAPE!

Moreover, the discrepancy becomes worse for Ecm < 7 MeV.

18O + 12C Excitation Function: Comparison with DC-TDHF

Fit experimental data with penetration of an inverted parabolic barrier (Wong formalism)

( )

−+= c

c VEE

Rωπωσ

2exp1ln

2

2

fmRc 51.088.22 ±=

MeVVc 14.062.7 ±=29.078.2 ±=ω

In the sub-barrier region DC-TDHF significantly under-predicts the cross-section

What can we learn from the emitted particles (protons, alphas, and neutrons)?

• The velocity (energy) distribution of the particles is described by a Maxwell-Boltzmann distribution

• If the gas is in equilibrium with the liquid then measuring the velocity (energy) distribution of gas particle teaches us about the temperature of the liquid

As the nucleus can be viewed as a charged droplet, measuring the energies of the emitted particles can provide information on the temperature of the nuclear system.

kTmv

evkT

mvf 223 2

42

)(−

= ππ

• Yield of α particles decreases as incident energy decreases.

• Distributions can be characterized by a first and second moment (average value and width).

First the yields…

The experimental α cross-section decreases as the bombarding energy decreases

At Ec.m. = 14 MeV, σα is close to σfusion As the bombarding energy decreases,

alpha emission becomes a smaller and smaller fraction of the fusion cross-section.

A statistical model, evapOR, that describes the de-excitation of excited nuclei does a poor job of describing the dependence of σα on bombarding energy.

• increases roughly linearly with increasing bombarding energy.

• σ(α) first increases linearly then appears to saturate with increasing bombarding energy.

• A statistical model (PACE4) does a reasonable job of describing the widths but under-predicts the average energy of the α particles.

Turning to the average energy and width of the distribution…

Conclusions We have developed an approach suitable to measure fusion excitation

functions with low intensity (radioactive) beams. Extraction of fusion cross-section for 20O+12C followed by charged particle

emission indicates an enhancement as compared to TDHF and Bass (+evapOR).

By implementing a gridless MCP, σfusion for 18O + 12C was measured to a level of 2 mb, one order of magnitude lower than previously known.

Comparison with the TDHF model indicates more quantum tunneling (thinner barrier)

Alpha particles emitted from the de-excitation of 30Si are more plentiful and energetic than predicted. Implications for structure of 30Si?

• Measure fusion excitation functions for neutron-rich light nuclei FSU: 18,19O + 12C ; GANIL: 20O + 12C; ReA3@MSU: heavier nuclei

Tracy Steinbach, Jon Schmidt, and Dr. Sylvie Hudan At Florida State University

Justin Vadas

Dr. V. Singh

Blake Wiggins

http://nuchem.iucf.Indiana.edu

Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6The Chart of the Nuclides and Terra IncognitaSlide Number 8Slide Number 9Fusion of Neutron-rich Light Nuclei Slide Number 11Slide Number 12Slide Number 13Slide Number 14SPIRAL@GANILA “simple” counting experimentSlide Number 17Slide Number 18Gridless MCP DetectorWhat do we want to measure?Method for Identifying Evaporation Residues18O + 12C Measurement at Florida State U.Si DetectorIdentifying Evaporation Residues18O + 12C Fusion Excitation Function18O + 12C Excitation Function: Comparison with DC-TDHF18O + 12C Excitation Function: Comparison with DC-TDHFSlide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32Slide Number 33Slide Number 34