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In low-energy nuclear structure, we have certain theories that work for certain types of nuclei, but there are some nuclei, called transitional nuclei, for which there is essentially no tractable theoretical description.

We can classify nuclei along a continuous scale from spherical through transitional to deformed nuclei. A nucleus's location on this scale can be estimated based on the product of the number of valence neutrons and protons (counting a hole as a positive number). When the product is small, the nucleus is spherical, when large, deformed.

The nuclear shell model, developed by Maria Goeppert Mayer in the 1950s, works very well for spherical nuclei. For deformed nuclei we also have good models, such as the cranked shell model with pairing. But for the intermediate case, transitional nuclei, there is basically nothing.

The closest thing to a working theory for transitional nuclei is the interacting boson model (IBM, also known as the interacting boson approximation, IBA). But the IBM has many adjustable parameters, especially for odd and odd-odd nuclei, and nobody knows how to predict these parameters a priori for a particular nucleus, so the model's predictive value is extremely limited.

More generally, this is an example of the quantum many-body system, where we need an effective approximation scheme. It's an odd situation, because we actually have an effective approximation scheme when the number of bodies (valence particles) is larger, but none for the case when it's intermediate. The state of ignorance is extreme, in the sense that we can't reliably predict even the simplest properties of transitional nuclei, such as the excitation energy of the first 2+ state in an even-even nucleus. We expect to have difficulties with many-body systems, but not to be as completely powerless as this. In a classical analogy, it would be as though we couldn't predict the future motion of the planets in our solar system, even on time-scales of hours. Another good comparison is with atomic physics, where there are tractable approximation schemes allowing extremely precise predictions, even for very large atoms.

I suspect that a lot of talented people would be deterred from working on this problem by an incorrect perception that it would require learning a lot of grotty details about nuclear forces. In fact, all the physical phenomena that are salient to this problem are generic phenomena for systems of fermions interacting through a short-range force. Experimentally, we see clusters of atoms that demonstrate the same "magic numbers" (shell closures) as clusters of neutrons and protons. If you could make progress on this problem for a toy model of identical fermions interacting through a delta-function potential, your work would almost certainly be immediately generalizable to nuclei.

In low-energy nuclear structure, we have certain theories that work for certain types of nuclei, but there are some nuclei, called transitional nuclei, for which there is essentially no tractable theoretical description.

We can classify nuclei along a continuous scale from spherical through transitional to deformed nuclei. A nucleus's location on this scale can be estimated based on the product of the number of valence neutrons and protons (counting a hole as a positive number). When the product is small, the nucleus is spherical, when large, deformed.

The nuclear shell model, developed by Maria Goeppert Mayer in the 1950s, works very well for spherical nuclei. For deformed nuclei we also have good models, such as the cranked shell model with pairing. But for the intermediate case, transitional nuclei, there is basically nothing.

The closest thing to a working theory for transitional nuclei is the interacting boson model (IBM, also known as the interacting boson approximation, IBA). But the IBM has many adjustable parameters, especially for odd and odd-odd nuclei, and nobody knows how to predict these parameters a priori for a particular nucleus, so the model's predictive value is extremely limited.

More generally, this is an example of the quantum many-body system, where we need an effective approximation scheme. It's an odd situation, because we actually have an effective approximation scheme when the number of bodies (valence particles) is larger, but none for the case when it's intermediate. The state of ignorance is extreme, in the sense that we can't reliably predict even the simplest properties of transitional nuclei, such as the excitation energy of the first 2+ state in an even-even nucleus. We expect to have difficulties with many-body systems, but not to be as completely powerless as this. In a classical analogy, it would be as though we couldn't predict the future motion of the planets in our solar system, even on time-scales of hours. Another good comparison is with atomic physics, where there are tractable approximation schemes allowing extremely precise predictions, even for very large atoms.

I suspect that a lot of talented people would be deterred from working on this problem by an incorrect perception that it would require learning a lot of grotty details about nuclear forces. In fact, all the physical phenomena that are salient to this problem are generic phenomena for systems of fermions interacting through an attractive short-range force. Experimentally, we see clusters of atoms that demonstrate the same "magic numbers" (shell closures) as clusters of neutrons and protons. If you could make progress on this problem for a toy model of identical fermions interacting through a delta-function potential, your work would almost certainly be immediately generalizable to nuclei.

In low-energy nuclear structure, we have certain theories that work for certain types of nuclei, but there are some nuclei, called transitional nuclei, for which there is essentially no tractable theoretical description.

We can classify nuclei along a continuous scale from spherical through transitional to deformed nuclei. A nucleus's location on this scale can be estimated based on the product of the number of valence neutrons and protons (counting a hole as a positive number). When the product is small, the nucleus is spherical, when large, deformed.

The nuclear shell model, developed by Maria Goeppert Mayer in the 1950s, works very well for spherical nuclei. For deformed nuclei we also have good models, such as the cranked shell model with pairing. But for the intermediate case, transitional nuclei, there is basically nothing.

The closest thing to a working theory for transitional nuclei is the interacting boson model (IBM, also known as the interacting boson approximation, IBA). But the IBM has many adjustable parameters, especially for odd and odd-odd nuclei, and nobody knows how to predict these parameters a priori for a particular nucleus, so the model's predictive value is extremely limited.

More generally, this is an example of the quantum many-body system, where we need an effective approximation scheme. It's an odd situation, because we actually have an effective approximation scheme when the number of bodies (valence particles) is larger, but none for the case when it's intermediate. The state of ignorance is extreme, in the sense that we can't reliably predict even the simplest properties of transitional nuclei, such as the excitation energy of the first 2+ state in an even-even nucleus. We expect to have difficulties with many-body systems, but not to be as completely powerless as this. In a classical analogy, it would be as though we couldn't predict the future motion of the planets in our solar system, even on time-scales of hours. Another good comparison is with atomic physics, where there are tractable approximation schemes allowing extremely precise predictions, even for very large atoms.

I suspect that a lot of talented people would be deterred from working on this problem by an incorrect perception that it would require learning a lot of grotty details about nuclear forces. In fact, all the physical phenomena that are salient to this problem are generic phenomena for systems of fermions interacting through a short-range force. Experimentally, we see clusters of atoms that demonstrate the same "magic numbers" (shell closures) as clusters of neutrons and protons. If you could make progress on this problem for a system of identical fermions interacting through a delta-function potential, your work would almost certainly be immediately generalizable to nuclei.

In low-energy nuclear structure, we have certain theories that work for certain types of nuclei, but there are some nuclei, called transitional nuclei, for which there is essentially no tractable theoretical description.

We can classify nuclei along a continuous scale from spherical through transitional to deformed nuclei. A nucleus's location on this scale can be estimated based on the product of the number of valence neutrons and protons (counting a hole as a positive number). When the product is small, the nucleus is spherical, when large, deformed.

The nuclear shell model, developed by Maria Goeppert Mayer in the 1950s, works very well for spherical nuclei. For deformed nuclei we also have good models, such as the cranked shell model with pairing. But for the intermediate case, transitional nuclei, there is basically nothing.

The closest thing to a working theory for transitional nuclei is the interacting boson model (IBM, also known as the interacting boson approximation, IBA). But the IBM has many adjustable parameters, especially for odd and odd-odd nuclei, and nobody knows how to predict these parameters a priori for a particular nucleus, so the model's predictive value is extremely limited.

More generally, this is an example of the quantum many-body system, where we need an effective approximation scheme. It's an odd situation, because we actually have an effective approximation scheme when the number of bodies (valence particles) is larger, but none for the case when it's intermediate. The state of ignorance is extreme, in the sense that we can't reliably predict even the simplest properties of transitional nuclei, such as the excitation energy of the first 2+ state in an even-even nucleus. We expect to have difficulties with many-body systems, but not to be as completely powerless as this. In a classical analogy, it would be as though we couldn't predict the future motion of the planets in our solar system, even on time-scales of hours. Another good comparison is with atomic physics, where there are tractable approximation schemes allowing extremely precise predictions, even for very large atoms.

I suspect that a lot of talented people would be deterred from working on this problem by an incorrect perception that it would require learning a lot of grotty details about nuclear forces. In fact, all the physical phenomena that are salient to this problem are generic phenomena for systems of fermions interacting through a short-range force. Experimentally, we see clusters of atoms that demonstrate the same "magic numbers" (shell closures) as clusters of neutrons and protons. If you could make progress on this problem for a toy model of identical fermions interacting through a delta-function potential, your work would almost certainly be immediately generalizable to nuclei.

In low-energy nuclear structure, we have certain theories that work for certain types of nuclei, but there are some nuclei, called transitional nuclei, for which there is essentially no tractable theoretical description.

We can classify nuclei along a continuous scale from spherical through transitional to deformed nuclei. A nucleus's location on this scale can be estimated based on the product of the number of valence neutrons and protons (counting a hole as a positive number). When the product is small, the nucleus is spherical, when large, deformed.

The nuclear shell model, developed by Maria Goeppert Mayer in the 1950s, works very well for spherical nuclei. For deformed nuclei we also have good models, such as the cranked shell model with pairing. But for the intermediate case, transitional nuclei, there is basically nothing.

The closest thing to a working theory for transitional nuclei is the interacting boson model (IBM, also known as the interacting boson approximation, IBA). But the IBM has many adjustable parameters, especially for odd and odd-odd nuclei, and nobody knows how to predict these parameters a priori for a particular nucleus, so the model's predictive value is extremely limited.

More generally, this is an example of the quantum many-body system, where we need an effective approximation scheme. It's an odd situation, because we actually have an effective approximation scheme when the number of bodies (valence particles) is larger, but none for the case when it's intermediate. The state of ignorance is extreme, in the sense that we can't reliably predict even the simplest properties of transitional nuclei, such as the excitation energy of the first 2+ state in an even-even nucleus. We expect to have difficulties with many-body systems, but not to be as completely powerless as this. In a classical analogy, it would be as though we couldn't predict the future motion of the planets in our solar system, even on time-scales of hours. Another good comparison is with atomic and molecular physics, where there are tractable approximation schemes allowing extremely precise predictions, even for very large systems.

In low-energy nuclear structure, we have certain theories that work for certain types of nuclei, but there are some nuclei, called transitional nuclei, for which there is essentially no tractable theoretical description.

We can classify nuclei along a continuous scale from spherical through transitional to deformed nuclei. A nucleus's location on this scale can be estimated based on the product of the number of valence neutrons and protons (counting a hole as a positive number). When the product is small, the nucleus is spherical, when large, deformed.

The nuclear shell model, developed by Maria Goeppert Mayer in the 1950s, works very well for spherical nuclei. For deformed nuclei we also have good models, such as the cranked shell model with pairing. But for the intermediate case, transitional nuclei, there is basically nothing.

The closest thing to a working theory for transitional nuclei is the interacting boson model (IBM, also known as the interacting boson approximation, IBA). But the IBM has many adjustable parameters, especially for odd and odd-odd nuclei, and nobody knows how to predict these parameters a priori for a particular nucleus, so the model's predictive value is extremely limited.

More generally, this is an example of the quantum many-body system, where we need an effective approximation scheme. It's an odd situation, because we actually have an effective approximation scheme when the number of bodies (valence particles) is larger, but none for the case when it's intermediate. The state of ignorance is extreme, in the sense that we can't reliably predict even the simplest properties of transitional nuclei, such as the excitation energy of the first 2+ state in an even-even nucleus. We expect to have difficulties with many-body systems, but not to be as completely powerless as this. In a classical analogy, it would be as though we couldn't predict the future motion of the planets in our solar system, even on time-scales of hours. Another good comparison is with atomic physics, where there are tractable approximation schemes allowing extremely precise predictions, even for very large atoms.

I suspect that a lot of talented people would be deterred from working on this problem by an incorrect perception that it would require learning a lot of grotty details about nuclear forces. In fact, all the physical phenomena that are salient to this problem are generic phenomena for systems of fermions interacting through a short-range force. Experimentally, we see clusters of atoms that demonstrate the same "magic numbers" (shell closures) as clusters of neutrons and protons. If you could make progress on this problem for a system of identical fermions interacting through a delta-function potential, your work would almost certainly be immediately generalizable to nuclei.