CHEM 441 Nuclear Shell Structure of unbound Excited States in Fluorine Research Paper

Rubric for CHEM 441/442 Research ReportThis rubric is provided to help you develop your final research report. This report should
1. Include an abstract
2. Present background information, discuss the motivation for your project, and state your
research question
3. Provide a detailed description of the procedures used to obtain your results
4. Present your results in a well-organized fashion
5. Draw appropriate conclusions and discuss how your results answer your research question
6. Contain an appendix that is your research notebook
Target Audience
The primary target audience for your report should be a student coming to work in your mentor’s
research lab next year. Think about what information has been important to your work and try to
present this in a way that would make sense to someone just starting. The secondary target audience is
faculty members and other researchers in the field that want to read a concise overview of your project.
Rubric (100 points total)
The following sections breakdown how each section of your report will be graded. The choice of citation
style is left to you and your research advisor. Be sure that the choice of citation style allows the reader
to easily find referenced works and is consistent throughout the report.
Introduction (20 points)

(12 – 20 points) The introduction provides background information that places the research in
context for a reader that is new to the field. It also clearly states the motivation for the research
and states the research question to be addressed by your project. References to articles or
previous work are clearly and consistently cited.
(6 – 12 points) The introduction provides background information that is not clearly connected
to the project or is difficult to understand for someone that is new to the field. The project’s
motivation is not clearly stated and/or the research question is vague or unclear. References are
not correctly cited.
(0 – 6 points) The introduction provides little to no background information and does not discuss
the motivation for the project. No research question is stated.
Procedures (20 points)

(12 – 20 points) Relevant procedures are clearly described such that someone with reasonable
lab competence could reproduce your work. Clear references are made to procedures detailed
elsewhere (e.g. in your appendix/lab notebook or a peer-reviewed publication)
(6 – 12 points) Procedures are not clearly described or are not relevant to the project.
References are not correctly cited.
(0 – 6 points) Procedures are not given or are poorly described.
Results (20 points)

(12 – 20 points) Results are clearly and appropriately presented and discussion is provided that
walks the reader through the data that each table/figure/graph/etc. is displaying and how it was
(6 – 12 points) Results are presented but the accompanying discussion does not clearly describe
what they are or how they were obtained
(0 – 6 points) Use of a different modality could more clearly present the results.
Conclusions (20 points)

(12 – 20 points) Conclusions are clearly stated and discussion justifying how they were drawn
from the data presented is given. If no conclusions can be drawn, this is stated and discussed.
The project’s outcome with respect to the research question is discussed. Future avenues of
investigation are mentioned if appropriate.
(6 – 12 points) Conclusions are stated but discussion does not clearly connect to the results
presented in order to justify the conclusions. Discussion does not clearly tie back to the research
(0 – 6 points) Conclusions are not clearly stated or are not given, and no mention of the original
research question is made.
Appendices (20 points)

(12 – 20 points) An organized lab notebook with entries relevant to the reported work is
attached as an appendix. Additional appendices describing relevant procedures/methods are
attached if appropriate. An ordered list of works cited throughout the report is included.
(6 – 12 points) Appendices do not clearly relate to the reported work. List of works cited does
not adhere to a consistent format.
(0 – 6 points) Appendices are absent or poorly organized.
Two- body edecay #1
Two- body edcay #2
Two- body edecay #3
Two- body edecay #4
I was to determnie the best fit for each graph by figuring out the the energy and widths that
worked the best. I started with two-body edecay graph #2. I kept the width at a fixed number so I
could determine the best energy. While determining the energy I realized x2 will drop until the
best energy is reached then curve back up. After finding the energy that fits best Idid the same
for the width. Now the energy is at a fixed number and so I can determine the best width. The
width was a little more complicated because the higher you go x2 still gets smaller. Looking at
the graph you can tell there’s a slight curve and then it starts looking like a line because not
much is dropping. For graph 1 the best energy was at 0.42 and around 3 for the best width.
Why are theorists excited about exotic nuclei?
Filomena M. Nunes
Citation: Physics Today 74, 5, 34 (2021); doi: 10.1063/PT.3.4748
View online:
View Table of Contents:
Published by the American Institute of Physics
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Why are
Quantum chromodynamics (QCD), that fundamental theory of the
strong force, is represented here as the root system of a tree. Through
effective-field theories for the nucleon–nucleon interaction (the tree’s
trunk) and through many-body methods (its branches), nuclear theory
can now connect QCD to the many nuclei nature produces (its fruits).
(Image by Orla/
Filomena Nunes ( is the
managing director of the FRIB Theory Alliance
and a professor of physics and astronomy, both
at Michigan State University in East Lansing.
Filomena M. Nunes
The limits of nuclear stability
provide deep insights into the
fundamental force responsible
for the presence of matter.
uclei are at the heart of all palpable matter.1
Although we understand the properties of things we
touch every day—from the carbon in our bodies
to the lanthanum in our cell phones—so much
more may be revealed by investigating elements at
the limits of their stability. Those limits become apparent when too
many neutrons or protons are added to a nucleus. Matter falls apart
in different ways, by emitting particles and radiation, say, or by
fissioning into much lighter elements. Indeed, the world’s elements
seem to be finely tuned as a subtle interplay of components of the
nuclear force. Those components can either hold a nucleus together
or doom it to nonexistence.
Collectively known as nucleons, neutrons and protons form the building blocks of nuclei. A nuclear isotope is characterized by a mass number A and charge
Z; each isotope contains Z protons and N = A–Z
neutrons. A few hundred isotopes exist naturally on
Earth. Many thousands of others are short-lived and
are constantly being created in numerous corners of
the universe.
Nuclear physics has always been an essential component of astrophysical phenomena. Roughly half of
the heavy elements found in our solar system originate from chain reactions triggered by neutron star
mergers or the violent collapse of massive stars. Exotic nuclei are created, if only for an instant. A major
ambition of our generation is to understand where
and how heavy matter forms.2 Exotic neutron-rich
nuclei are an essential piece of that puzzle.
Discerning the properties of nuclei and their reactions constitutes the research field known as lowenergy nuclear physics. At state-of-the-art facilities,
rare-isotope beams are produced by purifying the
shower of products of violent nuclear collisions between stable nuclei. Those isotopes are then either
stopped in traps for high-precision measurements
of their basic properties, such as mass and radius, or
sent to beamlines, where they interact with target nuclei to produce various reactions that provide crucial
information about the underlying force.
Despite the massive undertaking—from planning
and executing the experiments to interpreting their
results—those experiments are most often designed
to study one single isotope. Over the past five decades,
researchers have measured hundreds of isotopes
to fill in the so-called nuclear chart. Critics often
complain that what’s done in low-energy nuclear physics
amounts to mere stamp collecting. But the process is an important step to understanding how the world works: Simple patterns emerge from the chart, outlined in figure 1; and from
those patterns, we gather deep insights into the nuclear force
and predict new phenomena.
The theorists’ dream is to understand all the manifestations
of nuclear matter as it originates from fundamental forces—
strong, weak, electromagnetic, and gravitational. Nuclei are
primarily a consequence of the strong and electromagnetic
forces. But as its name implies, the strong force is so strong that
in many instances it cannot be treated as
a perturbation. Quantum chromodynamics
(QCD) explains how quarks come together
in triples to form neutrons and protons. Because a perturbative approach to QCD is not
applicable to neutrons, protons, or nuclei,
large-scale numerical computations are required, in which quarks are placed on a
lattice acted upon by the QCD Lagrangian.
(See the article by Carleton DeTar and Steven
Gottlieb, PHYSICS TODAY, February 2004,
page 45.)
Why don’t theorists calculate the properties of carbon-12 as a 36-quark problem or
those of uranium-238 as a 714-quark problem? That would be a more direct approach.
But the computations required to solve a
problem with even half a dozen quarks would
take years using the largest supercomputer
in the US. Evidently, simulating the vast majority of nuclei directly from QCD will remain a dream for the future.
Fortunately an alternative to QCD exists. The energy scale
of quarks is orders of magnitude higher than the energies required to determine the properties of nuclei, and there are wellcontrolled ways to connect the force between quarks with the
force between neutrons and protons. And through that connection, the theorists’ dream may become reality.
effective-field theory.4 Imagine you have an image with enormous resolution, but all you really need to know is whether a
giant gorilla sits at the center of the image. To that end, a lowresolution picture would suffice. Effective-field theory is the
tool a nuclear physicist would use to controllably blur the picture, reduce its complexity, and make the problem computationally tractable.
Effective-field theory averages out QCD interactions’ shortrange components not relevant to the physics of nuclei, and it
provides a form of the NN force using parameters that can be
determined directly from QCD. The resulting NN force can
FIGURE 1. NUCLEAR CHART of isotopes, plotted by atomic
number Z and neutron number N and color coded according to
the isotopes’ lifetimes. The inset shows a detail of the calcium and
scandium isotopic chains. The nuclear force is a consequence of the
quantum chromodynamic Lagrangian L. Identifying the patterns
that emerge from the isotopic chains yields a deeper understanding
of the nuclear force. (Image by Donna Padian.)
Connecting to the root
Nuclear theorists have long known that they do not need to explicitly include quarks in models to describe nuclear properties. Simply taking neutrons and protons as the building blocks
is enough to reproduce many features of known isotopes.
The effective force between neutrons and protons was traditionally determined through fits to a large body of nucleon–
nucleon (NN) data. Thanks to close collaborations between theorists and experimentalists over the decades, those fits had
improved enough by the end of the 1990s that the resulting NN
interactions perfectly described all relevant few-nucleon properties.3 Even so, no connection had been established between
the fundamental theory of QCD and the NN interaction from
which nuclei emerge. What was needed was a path to bridge
the effective NN interaction to fundamental interactions between quarks and gluons. Only through that transformation
could nuclear theory have a chance of evolving from a descriptive to a predictive science.
The path toward bridging nuclei with QCD was first introduced by Ubirajara (Bira) van Kolck and collaborators using
then be used to solve the nuclear many-body problem and calculate all relevant nuclear properties.
Limits of stability
Not all is settled in nuclear-force land. In the limits of stability,
theory encounters the most stringent tests. Such encounters are
why theorists should be excited about studies with exotic nuclei. Those nuclei have the answers; they detect when the theory is wrong.
Were there no Coulomb force, nuclei would come together
in pairs of neutrons and protons, because the interaction between those nucleons is slightly more attractive than either the
neutron–neutron interaction or the proton–proton interaction.
Because of the Coulomb repulsion between protons, as the system gets heavier, it needs more neutrons to provide the glue
that keeps the matter together. For example, the most stable
carbon isotope is 12C, with six neutrons and six protons, whereas
the most stable lead isotope is 208Pb, with 126 neutrons and
82 protons.
Nature produces isotopes with an asymmetry of neutrons
and protons much larger than 208Pb’s. But when the imbalance
becomes too large, the nucleus becomes unstable and decays,
either through nucleon emission or beta decay. In both cases
nature tries to restore the system’s stability with that decay. The
limits of stability, often referred to as the drip line, are determined by the last isotope, for which there is a bound state in a
given isotopic chain.
Strange things can happen at those limits: Nuclei, often
thought of as compact objects, can develop halos and extended
neutron skins (see, for example, reference 5). Lithium-11 is one
FIGURE 2. EXOTIC NUCLEI are quantum states at the limit of stability.
The potential V(r) between a nucleus’s core and a valence neutron a
distance r from the center is sketched in red. Classically, the neutron
would not be able to move outside the classically allowed region
(vertical dashed line). In stable nuclei, the valence neutron is well
bound: Its energy E0 is typically about −7 MeV and its wavefunction
(purple curve) dies quickly outside that region. The valence nucleon
for a nucleus at the limits of stability is loosely bound: Its energy E1 is
typically about −0.1 MeV and its wavefunction (blue curve) extends
well beyond the classically allowed region. (Image by Donna Padian.)
famous example. It is composed of a tightly bound core
(lithium-9) and two valence neutrons, which spend most of
their time away from the core and resemble a halo. An example
of an extended neutron skin is found in neutron-rich tin isotopes. Their valence neutron probability distribution extends
farther from the nuclear center than the proton distribution,
such that at the surface of the nucleus only neutrons exist.
Nuclei are quantum systems, and to a large extent one
can describe them by solving the nonrelativistic Schrödinger
equation. In the so-called valley of stability, the likelihood of
finding a valence neutron far from the center of mass of the nucleus is close to zero. But that is not the case for nuclei at the
limits of stability. Figure 2 contrasts a wavefunction of a valence
neutron in a stable nucleus with one in an unstable, loosely
bound nucleus.
In unstable isotopes, the valence neutron lives most of its
life in the classically forbidden region, far from the nuclear cen-
ter of mass. And it exhibits a characteristically long tail in its
wavefunction. Those long tails strongly imprint themselves on
the nucleons’ binding energies, radii, deformations, and electromagnetic responses.
In the early days of rare-isotope facilities, studies at the limit
of stability posed several challenges for theory. First, theorists
needed far greater precision in their calculations. The average energy per nucleon in 12C and 208Pb is about 7 MeV. However, if we look at the last bound isotope in an isotopic chain,
the typical energy that binds each valence nucleon is about
0.1 MeV. For studying stable nuclei, a theory with the precision
of 1 MeV is good enough. But when studying nuclei at the limits of stability, theorists need that precision to improve by an
order of magnitude.
Second, the traditional methods in many-body nuclear
physics simply could not capture long tails in the wavefunction
and fell short in their predictions. In the past decade, efforts to
develop many-body methods that can deal with loosely bound
systems have exploded. It used to be common for theorists to
expand the nuclear wavefunction into harmonic-oscillator basis
states—functions that fall off much faster than the known exponential dependence with radius—to exploit their analytic
advantages. But a revolution has recently taken place, with theorists introducing different bases to capture the long tails.
What’s more, with the enormous increase in computational
power, many-body methods have improved the scaling of computation time with mass number. At the turn of the millennium,
the largest ab initio many-body calculation could only calculate
the properties of nuclei up to 12C. But today, ab initio methods
can compute 132Sn, an extraordinary feat.6 And the precision of
the most competitive many-body ab initio approaches is now
nearing the 0.1 MeV standard.
The impressive progress in many-body methods has uncovered shortcomings in our understanding of the NN force. Although the precision has increased, the mismatch to experiment
at the limits of stability reveals a lack of accuracy in the interaction. It appears the blurry picture mentioned earlier is too
blurry to pick out the details one needs for barely bound systems. As it turns out, exactly at the limits of stability is where
small components of the NN force—those that are not significant for stable systems—become key.
Because the interaction is now rooted in QCD through effective field theory, ways now exist to improve the accuracy with
which the interaction is calculated. But the improvement comes
at the cost of some technical complications embodied in higherorder forces. Nevertheless, a courageous bunch of theorists are
tackling that work.
Probing nuclei with reactions
Ever since Ernest Rutherford’s gold-foil experiment, scientists
have used reactions to study nuclear properties. Now, more
than ever, that tool is essential. The rare isotopes we are interested in are unstable and will decay away if made into targets.
Fortunately, isotope factories are able to generate them in a
beam. Those isotopes then interact with a target that serves as
a probe.
Nuclear reactions are versatile tools because they offer various knobs to turn.7 On one hand, the energy at which the reaction takes place and the scattering angles that are measured
serve to adjust the penetrability of the beam. The energy and
angle variability allow experimentalists to scan a nucleus in a
way akin to tomography. As in positron emission tomography
(PET) scans, researchers may be able to create a three-dimensional
image of the nucleus.
On the other hand, depending on the choice of the particle
measured in the detector, one gets different information. When,
for example, the halo nucleus beryllium-11 collides with a 12C
target, many things may happen at the same time. Most of
the time the 11Be nucleus—composed of a well-bound 10Be core
and a valence neutron in a radially extended orbital—passes
through the target unscathed. But when 11Be does react, it may
remain in its ground state and yet suffer an elastically scattered
deflection. Or it may undergo an inelastic excitation, break up
into fragments, gain mass by picking up nucleons from the target, or even fuse with the target.
The type of detector that’s used determines the reaction
channel to be studied and the properties that can be extracted.
For example, to measure inelastic scattering, researchers examine the radiation from the de-excitation; from it they can extract
the probability that the transition between states in the halo
nucleus will occur.
Like nuclei themselves, nuclear reactions are ruled by quantum mechanics. As depicted in figure 3, the simple picture for
nuclear scattering consists of an incoming wave that impinges
on a target nucleus. The field generated by that target nucleus
distorts the incoming wave, and from that distortion one can
determine properties of the nucleus. The part of the wave deflected in the near side of the collision interferes with the part
deflected on the far side in a way that, to first order, is analogous
to the diffraction of light. The resulting pattern gives a measure
of the range of the relevant interaction.
Because the original wave can give rise to many other reaction channels, the intensity of the incoming wave will be reduced.7 We can think about the reaction process as being driven
by another sort of effective interaction—that between the two
reacting nuclei. That interaction is referred to as the optical potential, as it contains an imaginary component that removes
flux from the incoming wave. The process is analogous to what
happens when light is absorbed as it travels through a medium.
The fundamental theory for nuclear reactions is QCD. However, studying the reaction of 11Be and 12C isotopes from the
perspective of QCD is a daunting pursuit. The same effectivefield theories discussed earlier can help address the manybody scattering problem at hand. Such ab initio efforts to simulate nuclear reactions are ongoing, but they’re limited to light
systems.8 For heavier systems, another level of simplification
is required: casting the problem as a few-body problem and introducing the above-mentioned optical potential.
Although the theory that connects quark degrees of freedom to nucleon degrees of freedom is clean and straightforward,
albeit technologically challenging, the theory that goes from
the nucleon–nucleon interaction to the nucleus–nucleus interaction is less controlled and still largely phenomenological.
One of the greatest challenges in low-energy nuclear physics
is to make a formal connection to QCD, so that reaction theory
can become less dependent on data. In that respect, much work
remains to be done.9
Theory crosses borders
The physics of nuclei sits at the crossroads of many different research fields—from astrophysics to fundamental particle physics
and from chemistry to condensed-matter physics. Theory plays
a key role in establishing connections between those fields.
An important example of that interdisciplinarity is the research in fundamental symmetries at the interface between nuclear physics and high-energy physics. The quest for neutrinoless double beta decay, which tells us whether a neutrino is its
own antiparticle, will involve a giant detector (see PHYSICS
TODAY, January 2010, page 20). Accurate theoretical predictions
for the nuclear-structure properties of the relevant detecting
FIGURE 3. ELASTIC SCATTERING of a nucleus off a target is best described using waves: (a) Part of the incoming beam is deflected on the
near side of the target, whereas other parts are deflected on the far side. Because their paths differ, they have accumulated different phases
by the time they reach the detector. (b) The result at the detector is an interference pattern that’s directly related to the size of the target
nucleus. (Image by Donna Padian.)
The physics of nuclei sits
isotopes will be an essential ingredient for
the experiment’s success.
In many respects, nuclei can serve as test
beds of new physics beyond the standard
model. One example involving rare isotopes
has to do with baryon asymmetry in the
universe. The asymmetry can be explored
by searching for permanent electric dipole
moments10 in such pear-shaped nuclei as
radium-225 and protactinium-229. (See the
article by Norval Fortson, Patrick Sandars,
and Steve Barr, PHYSICS TODAY, June 2003,
page 33.)
The nuclear connection that has received
the most public attention is astrophysics. Since the first 10 seconds in the history of the cosmos, nuclei have shaped our universe. Nuclear reactions are the fuel for large astronomical objects, and through those reactions the universe has synthesized
the matter that pervades our lives. Nucleosynthesis, the chain
reactions by which nuclei are produced, occurs in stars and explosive environments such as supernovae and neutron star
mergers. In such extreme environments, nucleosynthesis steps
through many neutron-rich and proton-rich nuclei, and thus
their properties are important inputs to large-scale astrophysical simulations.
An illustration of the deep intersection between nuclear
physics and astrophysics is the first detection of gravitational
waves and their electromagnetic counterpart from the neutronstar merger GW170817. The electromagnetic signal offered an
independent constraint on the equation of state of neutron stars.11
The merger caused shivers in both the gravitational and nuclear communities. Often, reactions of astrophysical interest cannot be measured directly, and indirect reactions must be used
to probe the same information.12,13
The technical challenges in the theory of nuclei also cut
across fields. Nuclei are complex systems from which simple
phenomena emerge, just as in molecular physics.14 So it should
be no surprise that similar phenomena—halos, Efimov states,
deformation, phase transitions, and others—occur in the two
fields. Likewise, many-body methods are widely applied both
in chemistry and in nuclear physics; few-body methods that
describe reactions with molecules can also be used to study reactions of nuclei at the limits of stability. With efforts to make
nuclear theory more predictive, the field has been learning
from statistics to quantify uncertainties and to help with experimental design.15
at the crossroads of many
different research fields—
from astrophysics to
fundamental particle physics
and from chemistry to
condensed-matter physics.
Beyond stability
The mass frontier and the asymmetry frontier are both important in the theory of nuclei. As Z goes beyond around 100, at
some point the Coulomb repulsion becomes so strong that no
matter how many neutrons are used to glue a particular nucleus together, it becomes energetically more advantageous for
the isotope to either emit alpha particles or break apart and
decay into lighter nuclei. As theorists move toward ever larger
neutron–proton asymmetry, they also eventually reach a limit
in which valence nucleons are no longer able to stay attached
to the core nucleus. In both cases, theory needs to deal with the
effects of the continuum—the range of unbound states that
exist above a particle threshold.
Many large-mass isotopes are of interest to our society. The
mercury found in thermometers and barometers; the lead found
in weights and batteries; and 238U, the main fuel in reactors, all
spring to mind. Oganesson, the heaviest element in the periodic table, has Z = 118 and a lifetime of less than a millisecond.
Because of exponential growth in the computational cost in
ab initio many-body methods, theories for describing it and other
heavy systems rely on density functionals (see the article by
Andrew Zangwill, PHYSICS TODAY, July 2015, page 34).
Although informed by theory, the functionals are typically
fitted to experimental masses and other data. The models predict an island of stability of superheavy nuclei. (See the article
by Yuri T. Oganessian and Krzysztof P. Rykaczewski, PHYSICS
TODAY, August 2015, page 32.) Although the location of those
superheavy elements on the nuclear chart is uncertain, they
should reside above copernicium-112 on the neutron-rich side,
around N ≈ 184. The problem with phenomenological density
functional theories is that, despite their validity in regions
where data exist, they become unreliable in extrapolating to regions where no data exist. Although the path is complex, here,
too, theorists are trying to connect the density functionals to
more fundamental theories.
The second frontier concerns the neutron–proton asymmetry. For light nuclei, the most stable isotopes have a neutronto-proton ratio (N/Z) around one. With their increasing Coulomb
repulsion, heavier isotopes, such as 208Pb, reach N/Z = 1.5. But
near the limits of stability are exotic nuclei such as helium-8
(N/Z = 3) and 9C (N/Z = 0.5); long isotopic chains, such as Sn,
which has 32 isotopes; and neutron stars, the most perplexing
form of nuclear matter that exists, with N/Z of about 20. Precisely predicting the maximum number of neutrons that can be
added to a stable nucleus while keeping the system bound is
one of the greatest challenges for ab initio many-body theories,
especially for systems whose Z exceeds 20.
For nuclei with Z less than 20, the limits of stability have produced halos, in which valence nucleons hang around a central
core nucleus in the classically forbidden region, as discussed
earlier. Because the halo nucleons are decorrelated from the rest
of the nucleus, few-body theories—in which nuclei are composed of a core nucleus with few valence nucleons—are often
adequate to describe their properties.
When the attraction obtained by adding another neutron to
an isotopic chain is not enough to keep it bound, the nucleus
steps into the positive energy domain. States beyond the limits
of stability are sometimes elusive for theory, particularly if they
have short lifetimes. Examples of those states include the tetraMAY 2021 | PHYSICS TODAY 39
FIGURE 4. THE FACILITY for Rare Isotope Beams is taking shape as the highest-energy superconducting heavy-ion linear accelerator in the
world. When it begins operating in 2022, the facility will be able to accelerate all ions from hydrogen to uranium to at least 200 MeV/nucleon
and produce thousands of rare isotopes by in-beam fragmentation. (Courtesy of the Facility for Rare Isotope Beams.)
neutron,16 a hypothetical stable cluster of four neutrons; the
He resonance (N/Z = 5); and two-neutron radioactivity17 in 16Be.
New facilities
Around the world, technology to study rare isotopes has been
advancing rapidly. Many isotopes have been discovered since
the Rare Isotope Beam Factory began its operation a decade ago
at the RIKEN National Science Institute in Japan. But nuclear
physicists are most excited for the start of operations at the Facility for Rare Isotope Beams (FRIB) next year at Michigan State
University.18 That facility, partly shown in figure 4, is expected
to produce nearly 80% of all the isotopes predicted by density
functional theory, including many on the neutron dripline.
A linear accelerator bent into three segments, FRIB accelerates a heavy-ion primary beam up to half the speed of light.
Many different isotopes can be formed in the violent collisions
between nuclei in the beam and nuclei in the production target.
The rare isotopes of interest will be separated and either guided
directly into the relevant high-energy experimental halls, or
stopped and reaccelerated to the low-energy beamlines.
Nuclear facilities have been producing rare isotopes for
decades. Unique about FRIB is the 400 kW power of the accelerator. The increase in power expands the accelerator’s reach
into exotic areas: The machine will be able to explore the properties of long isotopic chains, such as the Sn isotopes, and thus
allow theorists to test their understanding of the NN interaction and its dependence on neutron–proton asymmetry. With
the beam’s intensity, FRIB will be able to measure several reaction channels simultaneously and more accurately than could
be done before. Along the way, FRIB will likely unveil some
unexpected phenomena to keep theorists scratching their heads.
This work was supported by NSF under grant PHY-1811815.
1. National Research Council, Nuclear Physics: Exploring the Heart of
Matter, National Academies Press (2013).
2. US Department of Energy Office of Science, Reaching for the Horizon: The 2015 Long Range Plan for Nuclear Science (2015).
3. R. Machleidt, Phys. Rev. C 63, 024001 (2001).
4. U. van Kolck, Nuclear Physics A 645, 273 (1999).
5. J. Al-Khalili, Halo Nuclei, Morgan & Claypool (2017).
6. V. Manea et al., Phys. Rev. Lett. 124, 092502 (2020).
7. I. J. Thompson, F. M. Nunes, Nuclear Reactions for Astrophysics:
Principles, Calculation and Applications of Low-Energy Reactions,
Cambridge U. Press (2009).
8. F. Raimondi et al., Phys. Rev. C 93, 054606 (2016).
9. C. W. Johnson et al., J. Phys. G: Nucl. Part. Phys. 47, 123001 (2020).
10. C. J. Lister, J. Butterworth, Nature 497, 190 (2013).
11. C. Horowitz, Ann. Phys. 411, 167992 (2019).
12. F. M. Nunes et al., Annu. Rev. Nucl. Part. Sci. 70, 147 (2020).
13. G. Potel et al., Eur. Phys. J. A 53, 178 (2017).
14. J. Lei et al., Phys. Rev. C 98, 051001 (2018).
15. G. B. King et al., Phys. Rev. Lett. 122, 232502 (2019).
16. K. Fossez et al., Phys. Rev. Lett. 119, 032501 (2017).
17. A. E. Lovell, F. M. Nunes, I. J. Thompson, Phys. Rev. C 95, 034605
18. T. Glasmacher et al., Nucl. Phys. News 27, 28 (2017).

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step 1
Upload your instructions
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
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How to get the most out of your experience with Writall
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
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Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.
Awesome service and amazing quality! I'll definitely be using it again when needed.
Customer 455113, November 15th, 2021
Amazing work!
Customer 454937, October 7th, 2021
Amazing job. Hellen Is fantastic
Customer 454983, December 9th, 2021
Computer science
A few dangling modifiers and the use of passive voice. But otherwise, good work
Customer 454513, September 29th, 2020
Thank you so much!!
Customer 454959, October 22nd, 2021
Perfect. Exactly what i needed
Customer 454937, October 25th, 2021
Thank you!
Customer 454959, February 6th, 2022
Best writer ever
Customer 454983, February 21st, 2022
Great paper and done before the deadline. Thank you
Customer 454659, October 20th, 2021
Huge help! Fantastic work!
Customer 454991, October 19th, 2021
very satisfied
Customer 454099, May 18th, 2020
Thanks so much! The writer did an excellent job!
Customer 454503, June 21st, 2020
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Current satisfaction rate
3 pages
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